What is the integral from 0 to pi of integral from 0 to pi/2 of cos(x+2y) ?

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integral from 0 to pi of integral from 0 to pi/2 of cos(x+2y)

\int_{0}^{π} \int_{0}^{\frac{π}{2}} cos (x + 2 y) d y d x

- 2

Solution steps

\int_{0}^{π} \int_{0}^{\frac{π}{2}} cos (x + 2 y) d y d x

\int_{0}^{\frac{π}{2}} cos (x + 2 y) d y = \frac{1}{2} (sin (x + π) - sin (x))

= \int_{0}^{π} \frac{1}{2} (sin (x + π) - sin (x)) d x

\int_{0}^{π} \frac{1}{2} (sin (x + π) - sin (x)) d x = - 2

= - 2

\int \int e^{- (x^{2} + y^{2})} d A

\int \int ln (x) d x d x

\int \int e^{2 x} d x d x

\int \int \int x^{2} d x d x d x

\int \int x y^{2} d x d y

What is the integral from 0 to pi of integral from 0 to pi/2 of cos(x+2y) ?
The integral from 0 to pi of integral from 0 to pi/2 of cos(x+2y) is -2