What is the integral from 2 to 3 of tsin(pit) ?

The integral from 2 to 3 of tsin(pit) is 5/pi

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integral from 2 to 3 of tsin(pit)

\int_{2}^{3} t sin (π t) d t

\frac{5}{π}

Decimal Notation

1.59154 \dots

Solution steps

\int_{2}^{3} 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]_{2}^{3}

= [- \frac{1}{π} t cos (π t) - \int - \frac{1}{π} cos (π t) d t]_{2}^{3}

\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))]_{2}^{3}

Simplify

= [- \frac{1}{π} t cos (π t) + \frac{1}{π ^{2}} sin (π t)]_{2}^{3}

Compute the boundaries:

\frac{5}{π}

= \frac{5}{π}

\int \frac{( x ^{5} - x ^{3} + 2 x )}{x ^{4}} d x

1 - e^{- t}

\int \frac{6 x ^{3} + 8 x}{x ^{4} - 16} d x

\frac{d y}{d x} = 6 x (y - 1)^{\frac{2}{3}}

\int \frac{x ^{3} - 6 x - 20}{x + 5} d x

What is the integral from 2 to 3 of tsin(pit) ?
The integral from 2 to 3 of tsin(pit) is 5/pi