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

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

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

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

2

Solution steps

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

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

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

= 1 + 1

Simplify

= 2

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