What is the integral from 0 to 1 of xarcsin(x) ?

The integral from 0 to 1 of xarcsin(x) is pi/8

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integral from 0 to 1 of xarcsin(x)

\int_{0}^{1} x arcsin (x) d x

\frac{π}{8}

Decimal Notation

0.39269 \dots

Solution steps

\int_{0}^{1} x arcsin (x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} arcsin (x) - \int \frac{x ^{2}}{2 1 - x ^{2}} d x]_{0}^{1}

= [\frac{1}{2} x^{2} arcsin (x) - \int \frac{x ^{2}}{2 1 - x ^{2}} d x]_{0}^{1}

\int \frac{x ^{2}}{2 1 - x ^{2}} d x = \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))

= [\frac{1}{2} x^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))]_{0}^{1}

Compute the boundaries:

\frac{π}{8}

= \frac{π}{8}

\frac{\partial}{\partial x} (3 x z)

\int \frac{8 e ^{x}}{e ^{2 x} - 16} d x

\int_{0}^{\frac{π}{2}} sin (2 θ) d θ

\frac{d}{d x} (3 ln (sec (x) + tan (x)))

y^{^{'}} - e^{x + 1} = 0

What is the integral from 0 to 1 of xarcsin(x) ?
The integral from 0 to 1 of xarcsin(x) is pi/8