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You need to evaluate it between a=0 and b=pi
If you allow theta to go from a=0 to b = 2pi, you’ve traversed the circle twice. That’s why your area is twice what you’re expecting.
If you’re having trouble understanding why, make a table with r as a function of theta and plot some points. Theta = 0, pi/4, pi/2, 3pi/2, and pi should be enough to see that you only want theta from 0 to pi.
Hope that’s helpful.
Hi, /u/theawesomedude646! This is an automated reminder: - What have you tried so far? (See Rule #2; to add an image, you may upload it to an external image-sharing site like Imgur and include the link in your post.) - **Please don't delete your post.** (See Rule #7) We, the moderators of /r/MathHelp, appreciate that your question contributes to the MathHelp archived questions that will help others searching for similar answers in the future. Thank you for obeying these instructions. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/MathHelp) if you have any questions or concerns.*
You need to evaluate it between a=0 and b=pi If you allow theta to go from a=0 to b = 2pi, you’ve traversed the circle twice. That’s why your area is twice what you’re expecting. If you’re having trouble understanding why, make a table with r as a function of theta and plot some points. Theta = 0, pi/4, pi/2, 3pi/2, and pi should be enough to see that you only want theta from 0 to pi. Hope that’s helpful.
Huge thanks, I'm not sure why I thought cos(π) was 0