(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Compute the indicated solid in POLAR COORDINATE using double integrals.

Below z = 4 - x^2 - y^2, z = x^2 + y^2, between y = x and y = 0.

2. Relevant equations

3. The attempt at a solution

First of all, the integrand is z = 4 - x^2-y^2 which in polar is 4 - r^2

The limit for the region D in polar is the intersections of y = x, y = 0 of the circle. To find that particular circle I think we have to solve the two z equations, which give us x^2 + y^2 = 2 in the end. This is a circle with radius 2

The limit of region D is 0 <= r <= sqrt(2), and for theta (i use x) is 0 <= x < pi/6

I am not sure whether pi/6 is really the intersecting point of y = x on the circle.... Please cofirm that...

This will give us the double integrals

integral (0 to pi/6) integral (0 to sqrt(2) (4 - r^2)r dr d theta

I think this give us pi/2 which is right from the book. But the book only gave pi/2 there is no work shown so I can't tell whether my work is right or not.

Please tell me if I am wrong in the limit of integrations.

Thankyou.

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# Homework Help: Another integration in polar

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