Answer:
The result of the integral is
Step-by-step explanation:
Polar coordinates:
In polar coordinates, we have that:
In which r is related to the radius values, while is related to the angles in the trigonometric circle.
In this question:
R is the region in the first quadrant
In the first quadrant in the trigonometric circles, the angles go from 0 to , which means that this are the outer limits of integration.
Between the circles with center the origin and radii 1 and 2
This means that the inner limits of integration are between 1 and 2.
The integral will be given by:
Inner integral:
By substituion,
So
= \frac{1}{2} \int_{1}^{2} \sin{u} du[/tex]
Integral of sine is minus cosine. So
Before replacing, we substitute back u.
Outer integral:
The result of the integral is
