What is the integral from 0 to pi/4 of 8/3 sin(x) ?

The integral from 0 to pi/4 of 8/3 sin(x) is (8-4sqrt(2))/3

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integral from 0 to pi/4 of 8/3 sin(x)

\int_{0}^{\frac{π}{4}} \frac{8}{3} sin (x) d x

\frac{8 - 4 2}{3}

Decimal

0.78104 \dots

Solution steps

\int_{0}^{\frac{π}{4}} \frac{8}{3} sin (x) d x

Take the constant out:

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

= \frac{8}{3} \cdot \int_{0}^{\frac{π}{4}} sin (x) d x

Use the common integral:

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

= \frac{8}{3} [- cos (x)]_{0}^{\frac{π}{4}}

Compute the boundaries:

- \frac{1}{2} + 1

= \frac{8}{3} (- \frac{1}{2} + 1)

Simplify

= \frac{8 - 4 2}{3}

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What is the integral from 0 to pi/4 of 8/3 sin(x) ?
The integral from 0 to pi/4 of 8/3 sin(x) is (8-4sqrt(2))/3