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

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

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

\int_{- π}^{π} t^{2} cos (t) d t

- 4 π

Decimal

- 12.56637 \dots

Solution steps

\int_{- π}^{π} t^{2} cos (t) d t

Apply Integration By Parts

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

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

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

Compute the boundaries:

- 4 π

= - 4 π

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