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

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

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

\int_{0}^{π} (sin (x) - cos (x)) d x

2

Solution steps

\int_{0}^{π} sin (x) - cos (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 (x) d x

\int_{0}^{π} sin (x) d x = 2

\int_{0}^{π} cos (x) d x = 0

= 2 - 0

Simplify

= 2

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