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

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

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

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

\frac{3 3}{2} + \frac{π}{3}

Decimal

3.64527 \dots

Solution steps

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

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

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

= \frac{3 3}{2} + \frac{π}{3}

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\int_{0}^{3} x^{2} + 3 x d x

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