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

The integral from 0 to t of 3t^3 is (3t^4)/4

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integral from 0 to t of 3t^3

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

\frac{3 t ^{4}}{4}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: [\frac{t ^{4}}{4}]_{0}^{t}

= 3 [\frac{t ^{4}}{4}]_{0}^{t}

Compute the boundaries:

\frac{t ^{4}}{4}

= 3 \cdot \frac{t ^{4}}{4}

Simplify

= \frac{3 t ^{4}}{4}

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What is the integral from 0 to t of 3t^3 ?
The integral from 0 to t of 3t^3 is (3t^4)/4