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

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

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integral from 0 to 1 of cos(ax)

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

\frac{sin ( a )}{a}

Solution steps

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

Apply u-substitution

: \int_{0}^{a} \frac{cos ( u )}{a} d u

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

Use the common integral:

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

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

Compute the boundaries:

sin (a)

= \frac{1}{a} sin (a)

Simplify

= \frac{sin ( a )}{a}

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