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

\int_{1}^{4} \frac{1}{x ( 1 + x )} d x

\int_{0}^{4} \frac{x}{1 + x} d x

\int_{- 1}^{3} ∣ 2 - x ∣ d x

\int_{0}^{1} x^{- 1} ln (x) d x

\int_{0}^{1} x ln (1 + x^{2}) d x

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