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

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}}

\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

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

\frac{d}{d x} (ln (x^{3} - 2 x^{2}))

\int cos (0)

y^{^{'}} = \frac{e ^{x + y}}{1 + e ^{x}}, y (1) = 0

\int 2^{2 - 2 x} d x

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