What is the integral from 0 to pi/4 of 2cos(x)+1 ?

The integral from 0 to pi/4 of 2cos(x)+1 is sqrt(2)+pi/4

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integral from 0 to pi/4 of 2cos(x)+1

\int_{0}^{\frac{π}{4}} 2 cos (x) + 1 d x

2 + \frac{π}{4}

Solution steps

\int_{0}^{\frac{π}{4}} 2 cos (x) + 1 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}{4}} 2 cos (x) d x + \int_{0}^{\frac{π}{4}} 1 d x

\int_{0}^{\frac{π}{4}} 2 cos (x) d x = 2

\int_{0}^{\frac{π}{4}} 1 d x = \frac{π}{4}

= 2 + \frac{π}{4}

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What is the integral from 0 to pi/4 of 2cos(x)+1 ?
The integral from 0 to pi/4 of 2cos(x)+1 is sqrt(2)+pi/4