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

The integral from 0 to pi/4 of (x+sin(x)) is (pi^2)/(32)-1/(sqrt(2))+1

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

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

\frac{π ^{2}}{32} - \frac{1}{2} + 1

Solution steps

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

\int_{0}^{\frac{π}{4}} x d x = \frac{π ^{2}}{32}

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

= \frac{π ^{2}}{32} - \frac{1}{2} + 1

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What is the integral from 0 to pi/4 of (x+sin(x)) ?
The integral from 0 to pi/4 of (x+sin(x)) is (pi^2)/(32)-1/(sqrt(2))+1