What is the integral from 0 to 1 of tsin(npit) ?

The integral from 0 to 1 of tsin(npit) is -((-1)^n)/(pin)

Popular >

integral from 0 to 1 of tsin(npit)

\int_{0}^{1} t sin (nπ t) d t

- \frac{( - 1 ) ^{n}}{πn}

Solution steps

\int_{0}^{1} t sin (nπ t) d t

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

- (- 1)^{n} \frac{1}{πn}

= - (- 1)^{n} \frac{1}{πn}

Simplify

= - \frac{( - 1 ) ^{n}}{πn}

\int_{1}^{3} (x^{2} + x) d x

\int_{1}^{10} x^{2} \frac{2}{81} (x - 1) d x

\int_{0}^{b} 8 e^{x} d x

\int_{- 1}^{8} x^{\frac{2}{3}} d x

\int_{0}^{2 π} - 3 sin^{2} (t) + 9 t d t

What is the integral from 0 to 1 of tsin(npit) ?
The integral from 0 to 1 of tsin(npit) is -((-1)^n)/(pin)