What is the integral from 0 to x of 3t^2 ?

The integral from 0 to x of 3t^2 is x^3

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integral from 0 to x of 3t^2

\int_{0}^{x} 3 t^{2} d t

x^{3}

Solution steps

\int_{0}^{x} 3 t^{2} d t

Take the constant out:

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

= 3 \cdot \int_{0}^{x} t^{2} d t

Apply the Power Rule

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

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

Compute the boundaries:

\frac{x ^{3}}{3}

= 3 \cdot \frac{x ^{3}}{3}

Simplify

= x^{3}

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What is the integral from 0 to x of 3t^2 ?
The integral from 0 to x of 3t^2 is x^3