Evaluating Repeated Integral: cos y sin x

[pfreemanjones]

Evaluate the following repeated integral:
[Pi/2]\int[/0][Pi/2]\int[/y]cos y sin x dx dy

 

[Apphysicist]

Have you ever encountered integration by iteration?

Also, you need to show your attempt at a solution.

 

[HallsofIvy]

This is
$$\int_{y=0}^{\pi/2}\int_{x= y}^{\pi/2}cos(y) sin(x)dy dx$$
$$= \int_{y= 0}^{\pi/2}cos(y)\left(\int_{x= y}^{2\pi} sin(x)dx\right)dy$$

Now, what is
$$\int_{x= y}^{\pi/2} sin(x)dx$$?