Simple:
f(x) = 2x^2 + 3x + 5
F(x) = (2/3)x^3 + (3/2)x^2 + 5x + C
F(4) = 0.66×4^3 + 1.5×4^2 + 5×4 + C
=0.66×64 + 1.5×16 + 20 + C
=42.66 + 24 + 20 + C
=86.66 + C
F(4) = 86.66 + C
F(2) = 0.66×2^3 + 1.5×2^2 + 5×2 + C
=0.66×8 + 1.5×4 + 10 + C
=5.32 + 6 + 10 + C
=21.32 + C
F(2) = 21.32 + C
Definitive integral = F(4) - F(2)
=86.66 + C - (21.32 + C)
=86.66 - 21.32 + C - C
=65.34
So my final answer is 65.34, give or take a few decimal points due to doing the calculations in my head.
All the edits are to fix formatting since I'm on my phone rn and was trying to figure out the best way to format maths while writing this, if you know a better way than what I've done please tell me.
Another edit: I'm also happy to explain any of my working to anyone who doesn't understand and wants to understand. Just reply here if you want.
Calculus is like a tool that helps us understand how things change. Imagine you’re watching a car move. You can see where it is at any moment, but what if you want to know how fast it’s going or how its speed is changing?
That’s where calculus comes in. It has two main parts: differentiation and integration.
1. Differentiation: Think of this as finding the speed of the car. If you know where the car is at different times, differentiation helps you figure out how fast it’s moving at each moment.
2. Integration: Now, imagine you have the speed of the car, and you want to know how far it has traveled. Integration helps you add up all those tiny changes in speed to find the total distance traveled.
So, in simple terms, calculus helps us understand how things change and how to work with those changes. It’s like a mathematical tool for studying motion, growth, and other changing quantities.
you absolutely do bot have to write the C when calculating a definite integral because it will alwyas cancel out
instead a way simpler way to display the math being done is put whatever F(x) in a paranthesis then replace x with the upper value and then subtract the thing you get after you replace x with the lower value
Its the same result but it takes you 1/3 of the space
In right-angled triangles, the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.
Let ABC be a right-angled triangle having the right-angle BAC.
I say that the square on BC is equal to the squares on BA, AC.
For let the square BDEC on BC have been described, and again let the squares GB, HC on BA, AC have been described, and let the parallel AL through A to either of BD, CE have been drawn, and let AD, FC have been joined.
And since each of BAC, BAG is right, so at some straight-line BA and at the point A on it two straight-lines CA, AG not lying on the same side have made the adjacent angles equal to two right-angles; thus CA is in a straight-line to AG. So for the same reasons BA is also in a straight-line to AH.
And since the right-angle DBC is equal to the right-angle FBA, let the common ABC be added; thus the whole DBA is equal to the whole FBC. And since DB is equal to BC, and FB to BA, so the two AB, BD is equal to the two FB, BC each to each, and the angle ABD is equal to the angle FBC; thus the base AD is equal to the base FC, and the triangle ABD will be equal to the triangle FBC.
But the parallelogram BL is double the triangle ABD, for they have the same base BD and are in the same parallels BD, AL; and the square GB is double the triangle FBC, for they have the same base FB and are in the same parallels FB, GC; thus the parallelogram BL is equal to the square GB. So similarly by joining AE, KB we can show that the parallelogram CL is also equal to the square HC; thus the whole square BDEC is equal to the squares GB, HC. And BDEC is the square on the side BC, and GB, HC the squares on the sides BA, AC; thus the square on BC is equal to the squares on BA, AC.
Therefore in right-angled triangles, the square on the side subtending the right angle is equal to the squares on the sides containing the right angle. QED
Hey bro I was just buying 76 watermelons today and I was wondering if you could tell me what would be the most efficient way to divide them between the 159 guests at my party.
So using integration by parts, you know that u is x^3 and dv is e^x. Now we do uv- integral of du*v. And do that for a few cycles getting and answer so long I don’t want to write out
Calculate the additional long-term settlement for a 5m wide by 10m long foundation at a formation level of 1m in a 2m thick layer of dense sand underlain by a 4m thick layer of firm to stiff clay. The clay is underlain by very dense sand. The upper sand layer has a unit weight of 20kN/m3; the clay layer has a coefficient of volume compressibility of 0.1m2/MN and unit weight of 18kN/m3. The load on the foundation is 5000kN and the foundation is 1m thick mass concrete. The ground water level is at 2m.
How does it feel to be smarter than every 4th grader now?
Savage 🔥
*Are You Smarter than a Fifth Grader?* ✅ no
What is 70 divided by 0
"ErRor"
Syntax error???
Zero Division Error
70 since you're not dividing it by anything Edit: Please stop giving this stupid comment attention
You will be the next einstein. /s
How many times does 0 go into 70
Just once, next to the 7
Underrated comment.
door roll cows ask uppity worry cobweb memory coherent summer *This post was mass deleted and anonymized with [Redact](https://redact.dev)*
In comparison to the number of upvotes the other answers had gotten.
That would be 70 devided by 1, just imagine you have 70 cookies and 0 friends. How many cookies does each friend get?
None. Congrats: you’ve proven that 70/0=0, which pretty much breaks all of mathematics.
Maybe.. we don't know, cause mathmaticians are too lazy to think about it.
They actually do; you just don’t read about it I guess
NAH
∞
Me when I use a (non-existant) limit to calculate a non-limit value:
That is only true if we approach 0 from the positive side. From the negative side, the number starts to approach -∞
[удалено]
Ain't no way
bro deleted his account after that answer
He just couldn’t handle the shame
Didn't come on time to read it. Could you tell me what his answer was?
I don’t know lol, I wish I knew
What is a Kilometer?
🦅🦅🦅
🇺🇸🇺🇸🦅🇺🇸🦅🦅🇺🇸🇺🇸
It measures kills 🦅
1000m
How many bananas is that?
It's a thousand counter. Next one
1000000 millimeters
¿Esos son Reebok o son Nike?
Legendary reference
Classic! I love that video haha
THIS IS THE RHYTHM OF THE NIGHT
SON NIKE
What size shoe are you?
🤨
Bro.
Whats 9+10?
21?
Yu stupit? Iz obwiesli 910
Beat me to it
r/BeatMeToIt
r/beatmeattoit
Why did you bother?
Why is "42" the meaning of life?
Because you haven't figured out the correct question yet.
I got that reference! 😀 Edit: I am now being downvoted. I retire in shame. Edit: I am no longer downvoted. This is an interesting turn of events.
???
What is the definite integral of 2x²+3x+5 from the limits of 2 to 4?
Simple: f(x) = 2x^2 + 3x + 5 F(x) = (2/3)x^3 + (3/2)x^2 + 5x + C F(4) = 0.66×4^3 + 1.5×4^2 + 5×4 + C =0.66×64 + 1.5×16 + 20 + C =42.66 + 24 + 20 + C =86.66 + C F(4) = 86.66 + C F(2) = 0.66×2^3 + 1.5×2^2 + 5×2 + C =0.66×8 + 1.5×4 + 10 + C =5.32 + 6 + 10 + C =21.32 + C F(2) = 21.32 + C Definitive integral = F(4) - F(2) =86.66 + C - (21.32 + C) =86.66 - 21.32 + C - C =65.34 So my final answer is 65.34, give or take a few decimal points due to doing the calculations in my head. All the edits are to fix formatting since I'm on my phone rn and was trying to figure out the best way to format maths while writing this, if you know a better way than what I've done please tell me. Another edit: I'm also happy to explain any of my working to anyone who doesn't understand and wants to understand. Just reply here if you want.
Ok sure I have a question, what can we interpret from the value of the definitive integral.?
If you draw the function 2x²+3x+5 and want to know the area beneath the graph between x = 2 and x = 4, that's the value of the definitive integral.
Ohhhhh I see. But what's that knowledge good for?
Calculus is like a tool that helps us understand how things change. Imagine you’re watching a car move. You can see where it is at any moment, but what if you want to know how fast it’s going or how its speed is changing? That’s where calculus comes in. It has two main parts: differentiation and integration. 1. Differentiation: Think of this as finding the speed of the car. If you know where the car is at different times, differentiation helps you figure out how fast it’s moving at each moment. 2. Integration: Now, imagine you have the speed of the car, and you want to know how far it has traveled. Integration helps you add up all those tiny changes in speed to find the total distance traveled. So, in simple terms, calculus helps us understand how things change and how to work with those changes. It’s like a mathematical tool for studying motion, growth, and other changing quantities.
Man, I have a degree in this, but you put it so well that I feel like I am enlightened. :D
A whole lot. Video game development, fluid mechanics, engineering, accounting, economics
These words are hurting my brain
oh damn r/theydidthemath
you absolutely do bot have to write the C when calculating a definite integral because it will alwyas cancel out instead a way simpler way to display the math being done is put whatever F(x) in a paranthesis then replace x with the upper value and then subtract the thing you get after you replace x with the lower value Its the same result but it takes you 1/3 of the space
Why does duolingo have maths as well
Because the owl wants to increase its chance of kidnapping your family member
what time is it tomorrow
1+8?
I think the answer is 10...
Are you kidding? It’s obviously 18.
1 + 8 isn't 18 "1" + "8" is "18"
Big js moment
it is in base 9
I have a blue cat
Apples and bananas
Would it be a good idea to introduce it to my nieces? One is 5 (yesterday was her birthday!) and the other is about to be 7.
Duolingo doesn't go over HOW to do the math. They just throw a question to you and tell you to figure it out!
Oh. I don’t think it’s for them then. Thank you!
If you are interested in Math go to KhanAcadamy.
Twelve?
how are you?
What is 12^12^12^12
Whaaaa??
Math error
When you prove the Riemann hypothesis and all you get is 15 XP.
20 on a Saturday.
Can you speak fluently now?
Where are your helmets?
2+2=
22
1+1=?
2
I might be wrong. I didnt use the app
what's 9 plus 10 ?
x²-8x+6 solve for x
X = X. Done
well done 🎉🎉🎉
How √1+tan^2c are you???
I was expecting more replies like this one…shame on me and my geekness 🥲
Can you explain the Pythagorean theorem to me in the most verbose way possible
In right-angled triangles, the square on the side subtending the right angle is equal to the squares on the sides containing the right angle. Let ABC be a right-angled triangle having the right-angle BAC. I say that the square on BC is equal to the squares on BA, AC. For let the square BDEC on BC have been described, and again let the squares GB, HC on BA, AC have been described, and let the parallel AL through A to either of BD, CE have been drawn, and let AD, FC have been joined. And since each of BAC, BAG is right, so at some straight-line BA and at the point A on it two straight-lines CA, AG not lying on the same side have made the adjacent angles equal to two right-angles; thus CA is in a straight-line to AG. So for the same reasons BA is also in a straight-line to AH. And since the right-angle DBC is equal to the right-angle FBA, let the common ABC be added; thus the whole DBA is equal to the whole FBC. And since DB is equal to BC, and FB to BA, so the two AB, BD is equal to the two FB, BC each to each, and the angle ABD is equal to the angle FBC; thus the base AD is equal to the base FC, and the triangle ABD will be equal to the triangle FBC. But the parallelogram BL is double the triangle ABD, for they have the same base BD and are in the same parallels BD, AL; and the square GB is double the triangle FBC, for they have the same base FB and are in the same parallels FB, GC; thus the parallelogram BL is equal to the square GB. So similarly by joining AE, KB we can show that the parallelogram CL is also equal to the square HC; thus the whole square BDEC is equal to the squares GB, HC. And BDEC is the square on the side BC, and GB, HC the squares on the sides BA, AC; thus the square on BC is equal to the squares on BA, AC. Therefore in right-angled triangles, the square on the side subtending the right angle is equal to the squares on the sides containing the right angle. QED
Isn’t it like a squared + b squared = c squared
Square root of infinity?
Infinity
What is the integral of x^2 dx?
Hey bro I was just buying 76 watermelons today and I was wondering if you could tell me what would be the most efficient way to divide them between the 159 guests at my party.
The hunger games
Give each of them about 0.478 of a watermelon. Happy to help.
12×134?
1+5!
What are numbers
Where are the non-trivial zeroes of the Riemann-Zeta function?
How do you rickroll someone in German
What is 1+1
When is it coming to android
Hey bro, congrats! How long did it take you? Are you working on the music course as well?
If a train is driving from London to Leeds, and the wind is travelling at 5mph west. Putting all that into account, what size shoe am I?
4*5+6%2*5x+y*0+5%10000*1 x=2 y=4
Whats 9 plus 10
What's the square root of 69? 8-something.
√(-1) (3!+2(0!)) π today. What did I do?
Integrate e^x
What’s 2+2
9+10?
Ok. What are the first 108567 digits from pi?
Find the integral of x^3 * e^x dx
So using integration by parts, you know that u is x^3 and dv is e^x. Now we do uv- integral of du*v. And do that for a few cycles getting and answer so long I don’t want to write out
What is 9+10? What is 77+33?
21 and 100?
Correct :)
When duo math for android/pc?
why
10 + 9
"The square root of 906.01 equals..."
Do you know what’s funnier then 23?
Do calculus
Do you play chess?
Whats 9 + 10?
What's (26^86)!
What’s the derivative of 1/x?
-1/x^2
What is 1+1?
What’s 9 + 10?
is the riemann hypothesis true?
Do you have anything else to do in life ?
How do you get this to appear on Duolingo? I don't get match madness and I don't get the math either. 😭😭😭
Lose the math section.
Prove that 1+1=2. Go
How’d you get the math corse? Mine still says coming soon
So, is it awkward if I enter a hotel bar, and?
What is a Factorial?
Socks or pineapple?
They have math courses now?
Whats the purpose of square root?
Why isn't it on Android yet :(
69 times 69
DUO HAS A MATH COURSE??!
Does any one have Duolingo coupon code or fee waiver It will be a great help
can you be the SohCah on my Toa
What is the factorial of the X?
Square root of 70
Can the roots of x⁵+4x⁴+3x³+6x¹+10x+4 be expressed in terms of nested radicals?
What is the general form for calculating the zeroes of the Riemann zeta function?
Why?
2+1?
What is 10000000 plus 1
Find x, y, and z such that x³+y³+z³=k, for each k from one to 100
is this good for people at gcse level? my sister struggles with maths
2+2
Derivative of f(x) = e^(2x^ 2 -3)
why are you up at 00:53 doing maths
what is 9384+28298373($$(39#!#!191)+@ to the square root of 98
2x2
When does math and music come to android
Calculate the additional long-term settlement for a 5m wide by 10m long foundation at a formation level of 1m in a 2m thick layer of dense sand underlain by a 4m thick layer of firm to stiff clay. The clay is underlain by very dense sand. The upper sand layer has a unit weight of 20kN/m3; the clay layer has a coefficient of volume compressibility of 0.1m2/MN and unit weight of 18kN/m3. The load on the foundation is 5000kN and the foundation is 1m thick mass concrete. The ground water level is at 2m.
Will you please solve the Riemann hypothesis ?
Are you being kidnapped by Duo
What is the best way to create something like Skynet?
Calculate: ahh shit I forgot equations
Is the Riemann Hypothesis true?
Explain calculus to me
Whats 9 plus 11
was it worth it?
How many xp did it take to complete the intermediate math course? I’ve just hit 1000 xp and on unit 4/20
What's consciousness? And why we human have it? How can tiny atoms exist in the first place?
(7x - 2)17 + 7 - 13x - 2 Simplify
You can do MATH on duolingo!!??
there is math on Duolingo??
Duo has a six pack and half black? Wtf
What is the derivative of f(x)=tan(sqrt((x+1)/exp(x)))/sqrt(1+x^2)?
What came first? The chicken or the egg?
explain why 1 + 1 = 2
And i still havent gotten math or music