What is the integral from 2 to 4 of xcos(x) ?

The integral from 2 to 4 of xcos(x) is 4sin(4)+cos(4)-2sin(2)-cos(2)

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integral from 2 to 4 of xcos(x)

\int_{2}^{4} x cos (x) d x

4 sin (4) + cos (4) - 2 sin (2) - cos (2)

Decimal

- 5.08330 \dots

Solution steps

\int_{2}^{4} x cos (x) d x

Apply Integration By Parts

= [x sin (x) - \int sin (x) d x]_{2}^{4}

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

= [x sin (x) - (- cos (x))]_{2}^{4}

Simplify

= [x sin (x) + cos (x)]_{2}^{4}

Compute the boundaries:

4 sin (4) + cos (4) - 2 sin (2) - cos (2)

= 4 sin (4) + cos (4) - 2 sin (2) - cos (2)

What is the integral from 2 to 4 of xcos(x) ?
The integral from 2 to 4 of xcos(x) is 4sin(4)+cos(4)-2sin(2)-cos(2)