What is the integral from 0 to pi of sin(6x+pi) ?

The integral from 0 to pi of sin(6x+pi) is 0

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integral from 0 to pi of sin(6x+pi)

\int_{0}^{π} sin (6 x + π) d x

0

Solution steps

\int_{0}^{π} sin (6 x + π) d x

Rewrite using trig identities

= \int_{0}^{π} - sin (6 x) d x

Take the constant out:

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

= - \int_{0}^{π} sin (6 x) d x

Apply u-substitution

: \int_{0}^{6 π} sin (u) \frac{1}{6} d u

= - \int_{0}^{6 π} sin (u) \frac{1}{6} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int_{0}^{6 π} sin (u) d u

Use the common integral:

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

= - \frac{1}{6} [- cos (u)]_{0}^{6 π}

Compute the boundaries:

0

= - \frac{1}{6} \cdot 0

Simplify

= 0

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What is the integral from 0 to pi of sin(6x+pi) ?
The integral from 0 to pi of sin(6x+pi) is 0