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Popular >

integral from 0 to 4 of x(4-x)

Solution

\int_{0}^{4} x (4 - x) d x

Solution

\frac{32}{3}

+1

Decimal

10.66666 \dots

Solution steps

\int_{0}^{4} x (4 - x) d x

Expand

x (4 - x) : 4 x - x^{2}

= \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}

Graph

Popular Examples

d y - (y - 1)^{2} = d x

tangent of f(x)=sqrt(x^2+9),\at x=4 tangent of

f (x) = x^{2} + 9, at x = 4

limit as h approaches 0 of 1

h \to 0 lim (1)

(dy)/(dt)(0.1)ty=6t

\frac{d y}{d t} (0.1) t y = 6 t

taylor \sqrt[4]{x},11 taylor

4 x, 11

Frequently Asked Questions (FAQ)

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