Question

Evaluate the given integral by changing to polar coordinates. sin(x2 y2) dA R , where R is the region in the first quadrant between the circles with center the origin and radii 2 and 4

Answer 1

Answer:

I = 1.47001

Step-by-step explanation:

we have the function

$f(x,y)=sin(x^2y^2)$

In polar coordinates we have

$x=rcos\theta\\y=rsin\theta$

and dA is given by

$dA=rdrd\theta$

Hence, the integral that we have to solve is

$I=\int \limt_2^4 \int \limit_0^{\pi /2}sin(r^4cos^2\theta sin^2\theta)rdrd\theta$

This integral can be solved in a convenient program of your choice (it is very difficult to solve in an analytical way, I use Wolfram Alpha on line)

I = 1.47001

Hope this helps!!!