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Popular >

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

Solution

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

Solution

\frac{32}{3}

+1

Decimal Notation

10.66666 \dots

Solution steps

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

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

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

= - \frac{64}{3} + 32

Simplify

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

= \frac{32}{3}

Popular Examples

derivative of arccos(5x^8)derivative of

arccos (5 x^{8})

derivative of (7x^2-1/x)

\frac{d}{d x} (\frac{7 x ^{2} - 1}{x})

y^{''}+4y=0,y(0)=1,y^'(0)=4

y^{^{''}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 4

(dy)/(dx)=32x^3y^3,y(0)=k

\frac{d y}{d x} = 32 x^{3} y^{3}, y (0) = k

integral of [(a^3)/(x^2+a^2)]^2

\int [\frac{a ^{3}}{x ^{2} + a ^{2}}]^{2} d x

Frequently Asked Questions (FAQ)

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