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

The integral from 0 to pi/2 of x^2 is (pi^3)/(24)

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integral from 0 to pi/2 of x^2

\int_{0}^{\frac{π}{2}} x^{2} d x

\frac{π ^{3}}{24}

Decimal

1.29192 \dots

Solution steps

\int_{0}^{\frac{π}{2}} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{\frac{π}{2}}

= [\frac{x ^{3}}{3}]_{0}^{\frac{π}{2}}

Compute the boundaries:

\frac{π ^{3}}{24}

= \frac{π ^{3}}{24}

\int_{4}^{6} (x^{2} + 2 x - 7) d x

\int_{\frac{3 π}{2}}^{π} x cos (x) d x

\int_{4}^{6} (x^{2} + 2 x - 6) d x

\int_{0}^{10} x e^{1 - x^{2}} d x

\int_{0}^{2 π} t cos (t) d t

What is the integral from 0 to pi/2 of x^2 ?
The integral from 0 to pi/2 of x^2 is (pi^3)/(24)