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

The integral from 0 to pi of x^3sin(x) is pi^3-6pi

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

\int_{0}^{π} x^{3} sin (x) d x

π^{3} - 6 π

Decimal Notation

12.15672 \dots

Solution steps

\int_{0}^{π} x^{3} sin (x) d x

Apply Integration By Parts

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

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

Simplify

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

Compute the boundaries:

π^{3} - 6 π

= π^{3} - 6 π

\int (1 - x^{2} - y^{2}) d y

x \to - 3 - lim (\frac{∣ x - 3 ∣}{x - 3})

\frac{d}{d x} (2 x^{3} + 4)

\int x + \frac{1}{x ^{2} + 1} d x

\frac{d}{d x} (e^{x} (x - 3))

What is the integral from 0 to pi of x^3sin(x) ?
The integral from 0 to pi of x^3sin(x) is pi^3-6pi