What is the integral from 0 to pi/2 of (2cos(x)-5x) ?

The integral from 0 to pi/2 of (2cos(x)-5x) is 2-(5pi^2)/8

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integral from 0 to pi/2 of (2cos(x)-5x)

\int_{0}^{\frac{π}{2}} (2 cos (x) - 5 x) d x

2 - \frac{5 π ^{2}}{8}

Decimal

- 4.16850 \dots

Solution steps

\int_{0}^{\frac{π}{2}} 2 cos (x) - 5 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}} 2 cos (x) d x - \int_{0}^{\frac{π}{2}} 5 x d x

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

\int_{0}^{\frac{π}{2}} 5 x d x = \frac{5 π ^{2}}{8}

= 2 - \frac{5 π ^{2}}{8}

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What is the integral from 0 to pi/2 of (2cos(x)-5x) ?
The integral from 0 to pi/2 of (2cos(x)-5x) is 2-(5pi^2)/8