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

The integral from 0 to t of xsin(x) is sin(t)-tcos(t)

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integral from 0 to t of xsin(x)

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

sin (t) - t cos (t)

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

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

Compute the boundaries:

sin (t) - t cos (t)

= sin (t) - t cos (t)

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