What is the integral from-1 to 1 of xsin(npix) ?

The integral from-1 to 1 of xsin(npix) is -(2(-1)^n)/(pin)

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integral from-1 to 1 of xsin(npix)

\int_{- 1}^{1} x sin (nπ x) d x

- \frac{2 ( - 1 ) ^{n}}{πn}

Solution steps

\int_{- 1}^{1} x sin (nπ x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

- (- 1)^{n} \frac{2}{πn}

= - (- 1)^{n} \frac{2}{πn}

Simplify

= - \frac{2 ( - 1 ) ^{n}}{πn}

\frac{\partial}{\partial t} (e^{- π t})

\frac{d}{d x} (tan (e^{7 x}) + e^{t a n (7 x)})

y^{^{'}} = 4 y + x^{2} + 7

\frac{u}{u ^{2} + 3}

\int x x + 1 d x

What is the integral from-1 to 1 of xsin(npix) ?
The integral from-1 to 1 of xsin(npix) is -(2(-1)^n)/(pin)