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

The integral from 0 to pi/2 of tcos(t) is pi/2-1

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integral from 0 to pi/2 of tcos(t)

\int_{0}^{\frac{π}{2}} t cos (t) d t

\frac{π}{2} - 1

Decimal Notation

0.57079 \dots

Solution steps

\int_{0}^{\frac{π}{2}} t cos (t) d t

Apply Integration By Parts

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

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

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

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

Simplify

= [t sin (t) + cos (t)]_{0}^{\frac{π}{2}}

Compute the boundaries:

\frac{π}{2} - 1

= \frac{π}{2} - 1

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What is the integral from 0 to pi/2 of tcos(t) ?
The integral from 0 to pi/2 of tcos(t) is pi/2-1