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

The integral from-pi to pi of x^2cos(x) is -4pi

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

\int_{- π}^{π} x^{2} cos (x) d x

- 4 π

Decimal Notation

- 12.56637 \dots

Solution steps

\int_{- π}^{π} x^{2} cos (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

- 4 π

= - 4 π

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

\int_{- 1}^{1} 2 cos (\frac{π}{3} x) d x

\int_{0}^{2} (x^{3}) d x

\int_{0}^{60} 100 e^{- 0.01 t} d t

\int_{1}^{x^{2}} 3 + t^{2} d t

What is the integral from-pi to pi of x^2cos(x) ?
The integral from-pi to pi of x^2cos(x) is -4pi