What is the integral from 0 to pi/2 of 6+3cos(x) ?

The integral from 0 to pi/2 of 6+3cos(x) is 3pi+3

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integral from 0 to pi/2 of 6+3cos(x)

\int_{0}^{\frac{π}{2}} 6 + 3 cos (x) d x

3 π + 3

Decimal

12.42477 \dots

Solution steps

\int_{0}^{\frac{π}{2}} 6 + 3 cos (x) 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}{2}} 6 d x + \int_{0}^{\frac{π}{2}} 3 cos (x) d x

\int_{0}^{\frac{π}{2}} 6 d x = 3 π

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

= 3 π + 3

\int_{0}^{6} \frac{1}{3} x e^{x} d x

\int_{2}^{- 2} (9 x + 8)^{2} d x

\int_{- 1}^{0} (x + 1) d x

\int_{- 1}^{3} 3 + 2 x - x^{2} d x

\int_{0}^{\frac{π}{4}} \frac{1}{cos ^{3} ( x )} d x

What is the integral from 0 to pi/2 of 6+3cos(x) ?
The integral from 0 to pi/2 of 6+3cos(x) is 3pi+3