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Popular Calculus >

integral from 0 to 4 of 4x^2-x^3

Solution

\int_{0}^{4} 4 x^{2} - x^{3} d x

Solution

\frac{64}{3}

+1

Decimal

21.33333 \dots

Solution steps

\int_{0}^{4} 4 x^{2} - x^{3} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{4} 4 x^{2} d x - \int_{0}^{4} x^{3} d x

\int_{0}^{4} 4 x^{2} d x = \frac{256}{3}

\int_{0}^{4} x^{3} d x = 64

= \frac{256}{3} - 64

Simplify

\frac{256}{3} - 64 : \frac{64}{3}

= \frac{64}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of 4x^2-x^3 ?
The integral from 0 to 4 of 4x^2-x^3 is 64/3