What is the integral from 0 to 4 of xsin(x) ?

The integral from 0 to 4 of xsin(x) is sin(4)-4cos(4)

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integral from 0 to 4 of xsin(x)

\int_{0}^{4} x sin (x) d x

sin (4) - 4 cos (4)

Solution steps

\int_{0}^{4} x sin (x) d x

Apply Integration By Parts

: [- x cos (x) - \int - cos (x) d x]_{0}^{4}

= [- x cos (x) - \int - cos (x) d x]_{0}^{4}

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

= [- x cos (x) - (- sin (x))]_{0}^{4}

Simplify

= [- x cos (x) + sin (x)]_{0}^{4}

Compute the boundaries:

sin (4) - 4 cos (4)

= sin (4) - 4 cos (4)

\int_{0}^{3} 5 (1 - e^{y}) d y

\int_{\frac{π}{3}}^{π} cos (x + \frac{π}{3}) d x

\int_{0}^{1} 17 x^{3} 1 - x^{2} d x

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

\int_{0}^{2} 2 x^{2} - 4 x d x

What is the integral from 0 to 4 of xsin(x) ?
The integral from 0 to 4 of xsin(x) is sin(4)-4cos(4)