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

The integral from 0 to 2 of xsin(x) is sin(2)-2cos(2)

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integral from 0 to 2 of xsin(x)

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

sin (2) - 2 cos (2)

Decimal

1.74159 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

= [- x cos (x) - (- sin (x))]_{0}^{2}

Simplify

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

Compute the boundaries:

sin (2) - 2 cos (2)

= sin (2) - 2 cos (2)

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos^{5} (x) d x

\int_{- 1}^{0} 2 x d x

\int_{0}^{\frac{π}{2}} cos (n x) d x

\int_{0}^{\frac{24}{25}} 1 + 25 x d x

\int_{1}^{4} e^{- x} (x - 1) d x

What is the integral from 0 to 2 of xsin(x) ?
The integral from 0 to 2 of xsin(x) is sin(2)-2cos(2)