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

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

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

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

2

Solution steps

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

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

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

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

= 1 + 1

Simplify

= 2

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