What is the integral from 0 to 1 of x*sin(pix) ?

The integral from 0 to 1 of x*sin(pix) is 1/pi

Popular >

integral from 0 to 1 of x*sin(pix)

\int_{0}^{1} x \cdot sin (π x) d x

\frac{1}{π}

Decimal Notation

0.31830 \dots

Solution steps

\int_{0}^{1} x sin (π x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

\frac{1}{π}

= \frac{1}{π}

y = sec (3 x^{4} + 5)

θ \to 0 lim (\frac{cos ( θ ) - 1}{θ})

\int_{0}^{2} π (\frac{1}{x + 4})^{2} d x

\frac{x ^{2}}{y ^{2} - 5} \frac{d y}{d x} = \frac{1}{2 y}

f (x) = ln (81 sin^{2} (x))

What is the integral from 0 to 1 of x*sin(pix) ?
The integral from 0 to 1 of x*sin(pix) is 1/pi