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

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

Popular >

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

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

- 2 π + 1

Decimal Notation

- 5.28318 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

- 2 π + 1

= - 2 π + 1

\int_{0}^{3} x^{2} e^{x^{3}} d x

\int_{0}^{π} - 2 cos^{2} (x) sin (x) d x

\int_{2}^{x} \frac{1}{ln ( t )} d t

\int_{0}^{1} 3 cos (\frac{π x}{2}) d x

\int_{0}^{1} x^{2} (1 + 2 x^{3})^{3} d x

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