What is the integral from 0 to pi/2 of 2/3 sin(θ) ?

The integral from 0 to pi/2 of 2/3 sin(θ) is 2/3

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integral from 0 to pi/2 of 2/3 sin(θ)

\int_{0}^{\frac{π}{2}} \frac{2}{3} sin (θ) d θ

\frac{2}{3}

Decimal

0.66666 \dots

Solution steps

\int_{0}^{\frac{π}{2}} \frac{2}{3} sin (θ) d θ

Take the constant out:

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

= \frac{2}{3} \cdot \int_{0}^{\frac{π}{2}} sin (θ) d θ

Use the common integral:

\int sin (θ) d θ = - cos (θ)

= \frac{2}{3} [- cos (θ)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= \frac{2}{3} \cdot 1

Simplify

= \frac{2}{3}

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What is the integral from 0 to pi/2 of 2/3 sin(θ) ?
The integral from 0 to pi/2 of 2/3 sin(θ) is 2/3