What is the integral from 0 to pi/4 of (xcos(x)+5) ?

The integral from 0 to pi/4 of (xcos(x)+5) is pi/(4sqrt(2))+1/(sqrt(2))-1+(5pi)/4

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integral from 0 to pi/4 of (xcos(x)+5)

\int_{0}^{\frac{π}{4}} (x cos (x) + 5) d x

\frac{π}{4 2} + \frac{1}{2} - 1 + \frac{5 π}{4}

Decimal

4.18945 \dots

Solution steps

\int_{0}^{\frac{π}{4}} x cos (x) + 5 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}{4}} x cos (x) d x + \int_{0}^{\frac{π}{4}} 5 d x

\int_{0}^{\frac{π}{4}} x cos (x) d x = \frac{π}{4 2} + \frac{1}{2} - 1

\int_{0}^{\frac{π}{4}} 5 d x = \frac{5 π}{4}

= \frac{π}{4 2} + \frac{1}{2} - 1 + \frac{5 π}{4}

What is the integral from 0 to pi/4 of (xcos(x)+5) ?
The integral from 0 to pi/4 of (xcos(x)+5) is pi/(4sqrt(2))+1/(sqrt(2))-1+(5pi)/4