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

\int_{1}^{7} ∣ sin (x) ∣ d x

\int_{0}^{1} (1 - x) sin (nπ x) d x

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

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

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

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