## anonymous 5 years ago Find the area of the region that lies inside both circles r=sin(theta) and r=cos(theta

1. anonymous

is this in polar coordinates?

2. anonymous

yes

3. anonymous

$A=2\int\limits_{0}^{\pi/4}1/2\sin^2\theta d \theta=\int\limits_{0}^{\pi/4}1/2(1-\cos2\theta)d \theta$ $=1/2[\theta-1/2\sin2\theta]_{0}^{\pi/4}={1 \over 8} \pi - {1 \over 4}$

4. anonymous

@AnwarA: How'd you get that answer, if I may ask?

5. anonymous

From what I've gathered, we can see that the point of intersection is at (theta)=π/4. Then we can get one integral of 1/2 * sin^2(theta) from 0 to π/4, added to an integral of 1/2 * cos^2(theta) from π/4 to π/2. Wouldn't that be enough to account for both halves of the petal-like enclosed shape?

6. anonymous

Alright, so we've gotten exactly the same answers...xD But can you show me how they're the same? I haven't done polar curves yet and I'm curious.

7. anonymous

well you're integrating twice over the same region sinx from 0 to pi/4

8. anonymous

the same area*

9. anonymous

that's why I multiplied the integral by 2.. make sense?

10. anonymous

Yep, I see now. Thanks. :)

11. anonymous

no problem :)

12. anonymous

you haven't done polar curves? you still in high school?

13. anonymous

or maybe a freshman?

14. anonymous

I'm a junior in AP Calc, polar curves is what we're doing immediately after we finish sequences & series. I skipped pre-calc, so now I'm pretty much going through the rest of the syllabus on my own to cover anything I missed.

15. anonymous

I see. wish you the best!

16. anonymous

how did you find the point of intersection?

17. anonymous

Plot the two polar curves (or set the two equations equal to each other) and based on simple trigonometry, the angle at which they both equal each other is π/4. I think you'll see exactly what I mean when you graph it though.

18. anonymous

alright thank you, it makes sense. btw im review sequences and series right now for my calculus exam can you reccemend a video or website which covers the section well? thank you

19. anonymous

Here you have links of tons of different types of convergence tests, basic concepts; basically anything you could want to see about these. :) No problem, http://tutorial.math.lamar.edu/Classes/CalcII/SeriesIntro.aspx