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

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

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

\int_{0}^{π} sin (x) + cos (2 x) d x

2

Solution steps

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

\int_{0}^{π} sin (x) d x = 2

\int_{0}^{π} cos (2 x) d x = 0

= 2 + 0

Simplify

= 2

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\int \frac{e ^{2 x}}{1 - e ^{x}} d x

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