What is the integral from 0 to pi of sin(xy) ?

The integral from 0 to pi of sin(xy) is (-cos(piy)+1)/y

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integral from 0 to pi of sin(xy)

\int_{0}^{π} sin (x y) d x

\frac{- cos ( π y ) + 1}{y}

Solution steps

\int_{0}^{π} sin (x y) d x

Apply u-substitution

: \int_{0}^{y π} \frac{sin ( u )}{y} d u

= \int_{0}^{y π} \frac{sin ( u )}{y} d u

Take the constant out:

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

= \frac{1}{y} \cdot \int_{0}^{y π} sin (u) d u

Use the common integral:

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

= \frac{1}{y} [- cos (u)]_{0}^{y π}

Compute the boundaries:

- cos (π y) + 1

= \frac{1}{y} (- cos (π y) + 1)

Simplify

= \frac{- cos ( π y ) + 1}{y}

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\int_{0}^{2} (2 - t)^{2} t^{3} d t

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

What is the integral from 0 to pi of sin(xy) ?
The integral from 0 to pi of sin(xy) is (-cos(piy)+1)/y