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

The integral from 0 to pi/2 of x^2*cos(x) is (pi^2)/4-2

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

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

\frac{π ^{2}}{4} - 2

Decimal Notation

0.46740 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

\frac{π ^{2}}{4} - 2

= \frac{π ^{2}}{4} - 2

\int_{0}^{1} x^{2} \cdot 1 - x^{2} d x

\int_{0}^{5} (4 - x^{2}) d x

\int_{e}^{6} \frac{1}{x ln ( x )} d x

\int_{1}^{2} 2 x - x^{2} d x

\int_{0}^{1} 4 e^{- 2 x} d x

What is the integral from 0 to pi/2 of x^2*cos(x) ?
The integral from 0 to pi/2 of x^2*cos(x) is (pi^2)/4-2