What is the integral from-1 to 1 of x^3sin(x) ?

The integral from-1 to 1 of x^3sin(x) is 10cos(1)-6sin(1)

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integral from-1 to 1 of x^3sin(x)

\int_{- 1}^{1} x^{3} sin (x) d x

10 cos (1) - 6 sin (1)

Solution steps

\int_{- 1}^{1} x^{3} sin (x) d x

Apply Integration By Parts

: [- x^{3} cos (x) - \int - 3 x^{2} cos (x) d x]_{- 1}^{1}

= [- x^{3} cos (x) - \int - 3 x^{2} cos (x) d x]_{- 1}^{1}

\int - 3 x^{2} cos (x) d x = - 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))

= [- x^{3} cos (x) - (- 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))))]_{- 1}^{1}

Simplify

= [- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))]_{- 1}^{1}

Compute the boundaries:

10 cos (1) - 6 sin (1)

= 10 cos (1) - 6 sin (1)

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\int_{1}^{3} x^{\frac{3}{2}} d x

\int_{0}^{x} f (t) (x - t) d t

What is the integral from-1 to 1 of x^3sin(x) ?
The integral from-1 to 1 of x^3sin(x) is 10cos(1)-6sin(1)