What is the integral from 0 to 2pi of tsin(t) ?

The integral from 0 to 2pi of tsin(t) is -2pi

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integral from 0 to 2pi of tsin(t)

\int_{0}^{2 π} t sin (t) d t

- 2 π

Decimal

- 6.28318 \dots

Solution steps

\int_{0}^{2 π} t sin (t) d t

Apply Integration By Parts

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

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

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

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

Simplify

= [- t cos (t) + sin (t)]_{0}^{2 π}

Compute the boundaries:

- 2 π

= - 2 π

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What is the integral from 0 to 2pi of tsin(t) ?
The integral from 0 to 2pi of tsin(t) is -2pi