What is the integral from 0 to x of 4x^3 ?

The integral from 0 to x of 4x^3 is x^4

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integral from 0 to x of 4x^3

\int_{0}^{x} 4 x^{3} d x

x^{4}

Solution steps

\int_{0}^{x} 4 x^{3} d x

Take the constant out:

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

= 4 \cdot \int_{0}^{x} x^{3} d x

Apply the Power Rule

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

= 4 [\frac{x ^{4}}{4}]_{0}^{x}

Compute the boundaries:

\frac{x ^{4}}{4}

= 4 \cdot \frac{x ^{4}}{4}

Simplify

= x^{4}

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What is the integral from 0 to x of 4x^3 ?
The integral from 0 to x of 4x^3 is x^4