What is the integral from 0 to 1 of sin(ax) ?

The integral from 0 to 1 of sin(ax) is (-cos(a)+1)/a

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integral from 0 to 1 of sin(ax)

\int_{0}^{1} sin (a x) d x

\frac{- cos ( a ) + 1}{a}

Solution steps

\int_{0}^{1} sin (a x) d x

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{a} [- cos (u)]_{0}^{a}

Compute the boundaries:

- cos (a) + 1

= \frac{1}{a} (- cos (a) + 1)

Simplify

= \frac{- cos ( a ) + 1}{a}

What is the integral from 0 to 1 of sin(ax) ?
The integral from 0 to 1 of sin(ax) is (-cos(a)+1)/a