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

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

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

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

0

Solution steps

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

\int_{0}^{\frac{π}{2}} sin (x) d x = 1

\int_{0}^{\frac{π}{2}} cos (x) d x = 1

= 1 - 1

Simplify

= 0

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