What is the integral from 0 to pi/3 of (cos(x)+1) ?

The integral from 0 to pi/3 of (cos(x)+1) is (sqrt(3))/2+pi/3

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integral from 0 to pi/3 of (cos(x)+1)

\int_{0}^{\frac{π}{3}} (cos (x) + 1) d x

\frac{3}{2} + \frac{π}{3}

Decimal

1.91322 \dots

Solution steps

\int_{0}^{\frac{π}{3}} 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}{3}} cos (x) d x + \int_{0}^{\frac{π}{3}} 1 d x

\int_{0}^{\frac{π}{3}} cos (x) d x = \frac{3}{2}

\int_{0}^{\frac{π}{3}} 1 d x = \frac{π}{3}

= \frac{3}{2} + \frac{π}{3}

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What is the integral from 0 to pi/3 of (cos(x)+1) ?
The integral from 0 to pi/3 of (cos(x)+1) is (sqrt(3))/2+pi/3