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

The integral from 0 to pi of sin(2x)+4sin(x) is 8

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

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

8

Solution steps

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

\int_{0}^{π} sin (2 x) d x = 0

\int_{0}^{π} 4 sin (x) d x = 8

= 0 + 8

Simplify

= 8

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What is the integral from 0 to pi of sin(2x)+4sin(x) ?
The integral from 0 to pi of sin(2x)+4sin(x) is 8