What is the integral from 0 to pi/2 of x^2sin(x) ?

The integral from 0 to pi/2 of x^2sin(x) is pi-2

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integral from 0 to pi/2 of x^2sin(x)

\int_{0}^{\frac{π}{2}} x^{2} sin (x) d x

π - 2

Decimal Notation

1.14159 \dots

Solution steps

\int_{0}^{\frac{π}{2}} x^{2} sin (x) d x

Apply Integration By Parts

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

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

\int - 2 x cos (x) d x = - 2 (x sin (x) + cos (x))

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

Simplify

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

Compute the boundaries:

π - 2

= π - 2

\frac{1}{( s + 2 ) ( s )}

\frac{e ^{- 0.1 s}}{s + 3}

\int \frac{sin ( x )}{1 + sin ( x )} d x

y^{^{'}} + (x + 2) y^{2} = 0

x \to \infty lim (\frac{2 x ^{2}}{x + 3})

What is the integral from 0 to pi/2 of x^2sin(x) ?
The integral from 0 to pi/2 of x^2sin(x) is pi-2