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

The integral from pi/2 to pi of 3x-sin(x) is (9pi^2)/8-1

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integral from pi/2 to pi of 3x-sin(x)

\int_{\frac{π}{2}}^{π} 3 x - sin (x) d x

\frac{9 π ^{2}}{8} - 1

Decimal Notation

10.10330 \dots

Solution steps

\int_{\frac{π}{2}}^{π} 3 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} 3 x d x - \int_{\frac{π}{2}}^{π} sin (x) d x

\int_{\frac{π}{2}}^{π} 3 x d x = \frac{9 π ^{2}}{8}

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

= \frac{9 π ^{2}}{8} - 1

\int \frac{x}{( x ^{2} - 1 ) [ ln ( x ^{2} - 1 ) ] ^{2}} d x

y^{^{'}} = 5 y^{2} sin (x)

\frac{d}{d x} (x^{c o t (x)})

\frac{\partial}{\partial y} (sin (\frac{x}{y}))

\int x^{2} - 13 d x

What is the integral from pi/2 to pi of 3x-sin(x) ?
The integral from pi/2 to pi of 3x-sin(x) is (9pi^2)/8-1