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Popular >

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

Solution

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

Solution

\frac{32}{3}

+1

Decimal Notation

10.66666 \dots

Solution steps

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

\int_{0}^{4} 4 x d x = 32

\int_{0}^{4} x^{2} d x = \frac{64}{3}

= 32 - \frac{64}{3}

Simplify

32 - \frac{64}{3} : \frac{32}{3}

= \frac{32}{3}

Popular Examples

integral of xcos((nxpi)/l)

\int x cos (\frac{n x π}{l}) d x

volumeabout y=0,x= 1/3 (y^2+2)^{3/2},[1,3]volume about

y = 0, x = \frac{1}{3} (y^{2} + 2)^{\frac{3}{2}}, [1, 3]

(dy)/(dx)=(3x)/(10y)

\frac{d y}{d x} = \frac{3 x}{10 y}

integral from 0 to 11 of 1/(121+x^2)

\int_{0}^{11} \frac{1}{121 + x ^{2}} d x

integral of e^{2x}x^2

\int e^{2 x} x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of 4x-x^2 ?
The integral from 0 to 4 of 4x-x^2 is 32/3