What is the integral from 0 to pi/5 of sin(5x) ?

The integral from 0 to pi/5 of sin(5x) is 2/5

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integral from 0 to pi/5 of sin(5x)

\int_{0}^{\frac{π}{5}} sin (5 x) d x

\frac{2}{5}

Decimal

0.4

Solution steps

\int_{0}^{\frac{π}{5}} sin (5 x) d x

Apply u-substitution

: \int_{0}^{π} sin (u) \frac{1}{5} d u

= \int_{0}^{π} sin (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{0}^{π} sin (u) d u

Use the common integral:

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

= \frac{1}{5} [- cos (u)]_{0}^{π}

Compute the boundaries:

2

= \frac{1}{5} \cdot 2

Simplify

= \frac{2}{5}

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What is the integral from 0 to pi/5 of sin(5x) ?
The integral from 0 to pi/5 of sin(5x) is 2/5