What is the integral from 1 to 2 of tsin(pit) ?

The integral from 1 to 2 of tsin(pit) is -3/pi

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integral from 1 to 2 of tsin(pit)

\int_{1}^{2} t sin (π t) d t

- \frac{3}{π}

Decimal Notation

- 0.95492 \dots

Solution steps

\int_{1}^{2} t sin (π t) d t

Apply Integration By Parts

: [- \frac{1}{π} t cos (π t) - \int - \frac{1}{π} cos (π t) d t]_{1}^{2}

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

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

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

Simplify

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

Compute the boundaries:

- \frac{3}{π}

= - \frac{3}{π}

\int_{1}^{a} \frac{1}{3 t ^{3}} d t

\int_{0}^{π} cos (x) \cdot sin (x) d x

\int_{- 2}^{0} \frac{2}{x ^{2} + 4 x + 8} d x

\int_{- 1}^{2} x + 2 x^{2} d x

\int_{2}^{4} \frac{x ^{3}}{x + 2} d x

What is the integral from 1 to 2 of tsin(pit) ?
The integral from 1 to 2 of tsin(pit) is -3/pi