What is the integral from 0 to pi of (5-sin(6x))/6 ?

The integral from 0 to pi of (5-sin(6x))/6 is (5pi)/6

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integral from 0 to pi of (5-sin(6x))/6

\int_{0}^{π} \frac{5 - sin ( 6 x )}{6} d x

\frac{5 π}{6}

Decimal

2.61799 \dots

Solution steps

\int_{0}^{π} \frac{5 - sin ( 6 x )}{6} d x

Take the constant out:

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

= \frac{1}{6} \cdot \int_{0}^{π} 5 - sin (6 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{6} (\int_{0}^{π} 5 d x - \int_{0}^{π} sin (6 x) d x)

\int_{0}^{π} 5 d x = 5 π

\int_{0}^{π} sin (6 x) d x = 0

= \frac{1}{6} (5 π - 0)

Simplify

\frac{1}{6} (5 π - 0) : \frac{5 π}{6}

= \frac{5 π}{6}

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What is the integral from 0 to pi of (5-sin(6x))/6 ?
The integral from 0 to pi of (5-sin(6x))/6 is (5pi)/6