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

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

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

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

\frac{1}{2} + \frac{π}{4}

Decimal

1.49250 \dots

Solution steps

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

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

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

= \frac{1}{2} + \frac{π}{4}

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