0
$\begingroup$

The questions is to find the area in the bounded region in polar coordinates

$r = \sqrt{\theta}$ from $3\pi/2$ to $2\pi$

Here is what I did: I got the integral of $\cfrac{1}{2}\theta d\theta$ from $3\pi/2$ to $2\pi$. Then I integrated and got $\cfrac {1}{4} \theta ^2$ from $3\pi/2$ to $2\pi$. As a result, I got $\cfrac {7}{16}\pi^2$

But I felt that there might be something wrong with my answer. Can someone tell me about this? Thanks

$\endgroup$
1
  • $\begingroup$ to find the area of the region in polar coordinates $\endgroup$ – Jaden Q Oct 21 '12 at 9:00
0
$\begingroup$

The area is $\cfrac12\displaystyle\int_{{3\pi}/2}^{2\pi} [r(\theta)]^2 d\theta = \cfrac12\displaystyle\int_{{3\pi}/2}^{2\pi} \theta d\theta$ and this should return $\cfrac{7}{8}\pi^2$. Check your work again.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.