What is the integral from 0 to pi/2 of xcos(y)(1-x) ?

The integral from 0 to pi/2 of xcos(y)(1-x) is x(1-x)

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integral from 0 to pi/2 of xcos(y)(1-x)

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

x (1 - x)

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

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

= (1 - x) x \cdot 1

Simplify

= x (1 - x)

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\int_{5}^{25} \frac{1}{x ( ln ( x ) ) ^{7}} d x

What is the integral from 0 to pi/2 of xcos(y)(1-x) ?
The integral from 0 to pi/2 of xcos(y)(1-x) is x(1-x)