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

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

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

\int_{0}^{π} sin (2) (x) d x

sin (2) \frac{π ^{2}}{2}

Decimal

4.48720 \dots

Solution steps

\int_{0}^{π} sin (2) x d x

Take the constant out:

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

= sin (2) \cdot \int_{0}^{π} x d x

Apply the Power Rule

= sin (2) [\frac{x ^{2}}{2}]_{0}^{π}

Compute the boundaries:

\frac{π ^{2}}{2}

= sin (2) \frac{π ^{2}}{2}

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