What is the integral from 6 to 7 of tsin(pit) ?

The integral from 6 to 7 of tsin(pit) is (13)/pi

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integral from 6 to 7 of tsin(pit)

\int_{6}^{7} t sin (π t) d t

\frac{13}{π}

Decimal Notation

4.13802 \dots

Solution steps

\int_{6}^{7} 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]_{6}^{7}

= [- \frac{1}{π} t cos (π t) - \int - \frac{1}{π} cos (π t) d t]_{6}^{7}

\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))]_{6}^{7}

Simplify

= [- \frac{1}{π} t cos (π t) + \frac{1}{π ^{2}} sin (π t)]_{6}^{7}

Compute the boundaries:

\frac{13}{π}

= \frac{13}{π}

\frac{d}{d x} (lo g_{12} (x^{2} + n x))

\frac{d}{d x} (2 sinh (\frac{x}{5}))

x \to 1 lim (\frac{x}{x ^{2} - 1})

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

\int \frac{1}{( x + 2 ) x ^{2} + 4 x} d x

What is the integral from 6 to 7 of tsin(pit) ?
The integral from 6 to 7 of tsin(pit) is (13)/pi