What is the integral from 0 to 1 of ax^2 ?

The integral from 0 to 1 of ax^2 is a/3

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integral from 0 to 1 of ax^2

\int_{0}^{1} a x^{2} d x

\frac{a}{3}

Solution steps

\int_{0}^{1} a x^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= a \cdot \int_{0}^{1} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{1}

= a [\frac{x ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= a \frac{1}{3}

Simplify

= \frac{a}{3}

\int_{0}^{2} \frac{8 x}{2 x ^{2} + 1} d x

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

\int_{1}^{8} x^{2} - 4 x - 12 d x

\int_{0}^{\frac{π}{2}} \frac{1}{3 - 2 cos ( x )} d x

\int_{0}^{t} t^{\frac{5}{2}} d t

What is the integral from 0 to 1 of ax^2 ?
The integral from 0 to 1 of ax^2 is a/3