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 Notation

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_{x}^{1} 6 (1 - y) d y

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\int_{1}^{\infty} \frac{4}{x ^{3}} 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