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 3 and 5

Using polar coordinates, the result of the integral is: .

The most used relation for polar coordinates is:

An integral in Cartesian coordinates is converted to polar using:

In this problem:

Thus:

The polar integral is:

The inner integral is:

Using substitution:

Applying the fundamental theorem of calculus:

Then, the outer integral is:

The result of the integral is .

A similar problem is given at link

In polar coordinates, the region is the set of points

and we have and . So the integral, converted to polar, is

Substitute to get

the answer is su.k.my? ? co.kc