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}}

= [- 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

\int_{0}^{l} x^{2} d x

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

\int_{0}^{2 π} 2 sin (t) d t

\int_{2}^{5} \frac{1}{x x ^{2} + 1} d x

\int_{5}^{9} \frac{x}{x + 4} d x

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