What is the integral from 0 to pi/2 of xsin(y) ?

The integral from 0 to pi/2 of xsin(y) is x

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integral from 0 to pi/2 of xsin(y)

\int_{0}^{\frac{π}{2}} x sin (y) d y

x

Solution steps

\int_{0}^{\frac{π}{2}} x sin (y) d y

Take the constant out:

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

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

Use the common integral:

\int sin (y) d y = - cos (y)

= x [- cos (y)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= x \cdot 1

Simplify

= x

\int_{- 1}^{0} 2 y + 2 d y

\int_{1}^{25} \frac{3}{x} d x

\int_{1}^{2} \frac{4 x}{1 + x ^{2}} d x

\int_{0}^{1} x e^{x + 2} d x

\int_{- 2}^{- 1} \frac{1}{( x + 1 ) ^{2}} d x

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