What is the integral from 0 to 1 of x*sin(x) ?

The integral from 0 to 1 of x*sin(x) is sin(1)-cos(1)

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integral from 0 to 1 of x*sin(x)

\int_{0}^{1} x \cdot sin (x) d x

sin (1) - cos (1)

Decimal

0.30116 \dots

Solution steps

\int_{0}^{1} x sin (x) d x

Apply Integration By Parts

= [- x cos (x) - \int - cos (x) d x]_{0}^{1}

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

= [- x cos (x) - (- sin (x))]_{0}^{1}

Simplify

= [- x cos (x) + sin (x)]_{0}^{1}

Compute the boundaries:

sin (1) - cos (1)

= sin (1) - cos (1)

What is the integral from 0 to 1 of x*sin(x) ?
The integral from 0 to 1 of x*sin(x) is sin(1)-cos(1)