What is the integral from 0 to pi/2 of 4sin(2x) ?

The integral from 0 to pi/2 of 4sin(2x) is 4

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integral from 0 to pi/2 of 4sin(2x)

\int_{0}^{\frac{π}{2}} 4 sin (2 x) d x

4

Solution steps

\int_{0}^{\frac{π}{2}} 4 sin (2 x) d x

Take the constant out:

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

= 4 \cdot \int_{0}^{\frac{π}{2}} sin (2 x) d x

Apply u-substitution

: \int_{0}^{π} sin (u) \frac{1}{2} d u

= 4 \cdot \int_{0}^{π} sin (u) \frac{1}{2} d u

Take the constant out:

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

= 4 \cdot \frac{1}{2} \cdot \int_{0}^{π} sin (u) d u

Use the common integral:

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

= 4 \cdot \frac{1}{2} [- cos (u)]_{0}^{π}

Simplify

4 \cdot \frac{1}{2} [- cos (u)]_{0}^{π} : 2 [- cos (u)]_{0}^{π}

= 2 [- cos (u)]_{0}^{π}

Compute the boundaries:

2

= 2 \cdot 2

Simplify

= 4

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