What is the integral from pi/2 to pi of x-sin(x) ?

The integral from pi/2 to pi of x-sin(x) is (3pi^2)/8-1

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integral from pi/2 to pi of x-sin(x)

\int_{\frac{π}{2}}^{π} x - sin (x) d x

\frac{3 π ^{2}}{8} - 1

Decimal Notation

2.70110 \dots

Solution steps

\int_{\frac{π}{2}}^{π} 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_{\frac{π}{2}}^{π} x d x - \int_{\frac{π}{2}}^{π} sin (x) d x

\int_{\frac{π}{2}}^{π} x d x = \frac{3 π ^{2}}{8}

\int_{\frac{π}{2}}^{π} sin (x) d x = 1

= \frac{3 π ^{2}}{8} - 1

\frac{d y}{d x} = \frac{3 x}{4 y}

sec (3 sin (2 x))

x \to 0 lim (e^{x} - 1)

(- 3, - 7), (2, 3)

\int \frac{1}{cos ^{2} ( s )} d s

What is the integral from pi/2 to pi of x-sin(x) ?
The integral from pi/2 to pi of x-sin(x) is (3pi^2)/8-1