What is the integral from 0 to pi of x^2cos(x) ?

The integral from 0 to pi of x^2cos(x) is -2pi

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integral from 0 to pi of x^2cos(x)

\int_{0}^{π} x^{2} cos (x) d x

- 2 π

Decimal Notation

- 6.28318 \dots

Solution steps

\int_{0}^{π} x^{2} cos (x) d x

Apply Integration By Parts

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

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

\int 2 x sin (x) d x = 2 (- x cos (x) + sin (x))

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

Compute the boundaries:

- 2 π

= - 2 π

\int \frac{4 x ^{2} + 13 x - 9}{x ^{3} + 2 x ^{2} - 3 x} d x

\frac{d y}{d t} + 3 y = cos (2 t), y (0) = - 1

\int \frac{a + b sin ^{3} ( t )}{cos ^{2} ( t )} d t

\int - 32 x d x

\int_{0}^{2} \frac{1}{x ^{2} - 6 x + 5} d x

What is the integral from 0 to pi of x^2cos(x) ?
The integral from 0 to pi of x^2cos(x) is -2pi