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

The integral from pi to (3pi)/2 of xsin(x) is -1-pi

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

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

- 1 - π

Decimal

- 4.14159 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

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

Compute the boundaries:

- 1 - π

= - 1 - π

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