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

The integral from pi/2 to (3pi)/2 of xsin(x) is -2

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integral from pi/2 to (3pi)/2 of xsin(x)

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

- 2

Solution steps

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

Apply Integration By Parts

: [- x cos (x) - \int - cos (x) d x]_{\frac{π}{2}}^{\frac{3 π}{2}}

= [- x cos (x) - \int - cos (x) d x]_{\frac{π}{2}}^{\frac{3 π}{2}}

\int - cos (x) d x = - sin (x)

= [- x cos (x) - (- sin (x))]_{\frac{π}{2}}^{\frac{3 π}{2}}

Simplify

= [- x cos (x) + sin (x)]_{\frac{π}{2}}^{\frac{3 π}{2}}

Compute the boundaries:

- 2

= - 2

\int_{2}^{3} \frac{x}{1 - x ^{2}} d x

\int_{2}^{6} x d x

\int_{1}^{3} (2 x - 1) d x

\int_{- 1}^{3} 2 x - x^{2} d x

\int_{0}^{π} sin (x) \cdot sin (n x) d x

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