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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

(\partial)/(\partial x)((x^2)/(y^3))

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

area x^2-1, 1/2 x^2 area

x^{2} - 1, \frac{1}{2} x^{2}

integral of (sin(2x))/(2+2sin^2(x))

\int \frac{sin ( 2 x )}{2 + 2 sin ^{2} ( x )} d x

y^{''}+49y=-49sec^2(7x)

y^{^{''}} + 49 y = - 49 sec^{2} (7 x)

(9x^2+y-1)-(4y-x)y^'=0

(9 x^{2} + y - 1) - (4 y - x) y^{^{'}} = 0

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