What is the integral from 0 to (3pi)/2 of (xsin(x)) ?

The integral from 0 to (3pi)/2 of (xsin(x)) is -1

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integral from 0 to (3pi)/2 of (xsin(x))

\int_{0}^{\frac{3 π}{2}} (x sin (x)) d x

- 1

Solution steps

\int_{0}^{\frac{3 π}{2}} x sin (x) d x

Apply Integration By Parts

: [- x cos (x) - \int - cos (x) d x]_{0}^{\frac{3 π}{2}}

= [- x cos (x) - \int - cos (x) d x]_{0}^{\frac{3 π}{2}}

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

= [- x cos (x) - (- sin (x))]_{0}^{\frac{3 π}{2}}

Simplify

= [- x cos (x) + sin (x)]_{0}^{\frac{3 π}{2}}

Compute the boundaries:

- 1

= - 1

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What is the integral from 0 to (3pi)/2 of (xsin(x)) ?
The integral from 0 to (3pi)/2 of (xsin(x)) is -1