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

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

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

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

x (1 - x)

Solution steps

\int_{0}^{\frac{π}{2}} x cos (y) (- x + 1) 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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What is the integral from 0 to pi/2 of xcos(y)(-x+1) ?
The integral from 0 to pi/2 of xcos(y)(-x+1) is x(1-x)