What is the integral from 0 to 5pi of x^3sin(x) ?

The integral from 0 to 5pi of x^3sin(x) is 125pi^3-30pi

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integral from 0 to 5pi of x^3sin(x)

\int_{0}^{5 π} x^{3} sin (x) d x

125 π^{3} - 30 π

Decimal Notation

3781.53680 \dots

Solution steps

\int_{0}^{5 π} x^{3} sin (x) d x

Apply Integration By Parts

: [- x^{3} cos (x) - \int - 3 x^{2} cos (x) d x]_{0}^{5 π}

= [- x^{3} cos (x) - \int - 3 x^{2} cos (x) d x]_{0}^{5 π}

\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))))]_{0}^{5 π}

Simplify

= [- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))]_{0}^{5 π}

Compute the boundaries:

125 π^{3} - 30 π

= 125 π^{3} - 30 π

π r^{2} h

\int x^{3} - 4 x d x

\int sin^{9} (x) cos^{5} (x) d x

\frac{d y}{d x} = \frac{x}{y ^{2}}

What is the integral from 0 to 5pi of x^3sin(x) ?
The integral from 0 to 5pi of x^3sin(x) is 125pi^3-30pi