What is the integral from 0 to pi of 8sin(x)-sin(8x) ?

The integral from 0 to pi of 8sin(x)-sin(8x) is 16

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integral from 0 to pi of 8sin(x)-sin(8x)

\int_{0}^{π} 8 sin (x) - sin (8 x) d x

16

Solution steps

\int_{0}^{π} 8 sin (x) - sin (8 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

= \int_{0}^{π} 8 sin (x) d x - \int_{0}^{π} sin (8 x) d x

\int_{0}^{π} 8 sin (x) d x = 16

\int_{0}^{π} sin (8 x) d x = 0

= 16 - 0

Simplify

= 16

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What is the integral from 0 to pi of 8sin(x)-sin(8x) ?
The integral from 0 to pi of 8sin(x)-sin(8x) is 16