What is the integral from 0 to 1 of tcos(pit) ?

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

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integral from 0 to 1 of tcos(pit)

\int_{0}^{1} t cos (π t) d t

- \frac{2}{π ^{2}}

Decimal Notation

- 0.20264 \dots

Solution steps

\int_{0}^{1} t cos (π t) d t

Apply Integration By Parts

: [\frac{1}{π} t sin (π t) - \int \frac{1}{π} sin (π t) d t]_{0}^{1}

= [\frac{1}{π} t sin (π t) - \int \frac{1}{π} sin (π t) d t]_{0}^{1}

\int \frac{1}{π} sin (π t) d t = - \frac{1}{π ^{2}} cos (π t)

= [\frac{1}{π} t sin (π t) - (- \frac{1}{π ^{2}} cos (π t))]_{0}^{1}

Simplify

= [\frac{1}{π} t sin (π t) + \frac{1}{π ^{2}} cos (π t)]_{0}^{1}

Compute the boundaries:

- \frac{2}{π ^{2}}

= - \frac{2}{π ^{2}}

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