What is the integral from-1 to 1 of xsin(x) ?

The integral from-1 to 1 of xsin(x) is -2cos(1)+2sin(1)

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integral from-1 to 1 of xsin(x)

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

- 2 cos (1) + 2 sin (1)

Decimal

0.60233 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

- 2 cos (1) + 2 sin (1)

= - 2 cos (1) + 2 sin (1)

\int_{0}^{1} 7 cos (\frac{π t}{2}) d t

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

\int_{0}^{4} x x^{2} + 10 d x

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

\int_{1}^{2} x^{2} + x d x

What is the integral from-1 to 1 of xsin(x) ?
The integral from-1 to 1 of xsin(x) is -2cos(1)+2sin(1)