What is the integral from 0 to pi of ysin(x) ?

The integral from 0 to pi of ysin(x) is y*2

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integral from 0 to pi of ysin(x)

\int_{0}^{π} y sin (x) d x

y \cdot 2

Solution steps

\int_{0}^{π} y sin (x) d x

Take the constant out:

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

= y \cdot \int_{0}^{π} sin (x) d x

Use the common integral:

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

= y [- cos (x)]_{0}^{π}

Compute the boundaries:

2

= y \cdot 2

\int_{- 1}^{2} x (\frac{x ^{2}}{3}) d x

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

\int_{0}^{2} (2 x - 3) (8 x^{2} + 4) d x

\int_{0}^{2} x \cdot sin (\frac{nπ x}{2}) d x

\int_{0}^{2} y e^{x y} d x

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