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Popular >

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 Notation

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}

Popular Examples

limit as x approaches 4+of x

x \to 4 + lim (x)

integral of ((12x+30))/((x^2+2x-8))

\int \frac{( 12 x + 30 )}{( x ^{2} + 2 x - 8 )} d x

integral of (x^3)/(x^2)

\int \frac{x ^{3}}{x ^{2}} d x

(\partial)/(\partial y)(4x^3y^{-2})

\frac{\partial}{\partial y} (4 x^{3} y^{- 2})

laplacetransform te^{-t}cos(t)laplace transform

t e^{- t} cos (t)

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