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Popular >

integral of x^2(4-x)

Solution

\int x^{2} (4 - x) d x

Solution

\frac{4 x ^{3}}{3} - \frac{x ^{4}}{4} + C

Solution steps

\int x^{2} (4 - x) d x

Expand

x^{2} (4 - x) : 4 x^{2} - x^{3}

= \int 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 4 x^{2} d x - \int x^{3} d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int x^{3} d x = \frac{x ^{4}}{4}

= \frac{4 x ^{3}}{3} - \frac{x ^{4}}{4}

Add a constant to the solution

= \frac{4 x ^{3}}{3} - \frac{x ^{4}}{4} + C

Popular Examples

limit as x approaches 2 of (4-x^2)/(2+x)

x \to 2 lim (\frac{4 - x ^{2}}{2 + x})

derivative of 20x-x^2

\frac{d}{d x} (20 x - x^{2})

(dx)/(dt)= 3/2 tcos^2(x),x(0)=-1.4

\frac{d x}{d t} = \frac{3}{2} t cos^{2} (x), x (0) = - 1.4

derivative of sqrt(x+1)+sqrt(x)

\frac{d}{d x} (x + 1 + x)

integral of 10sin^3(x)cos^5(x)

\int 10 sin^{3} (x) cos^{5} (x) d x

Frequently Asked Questions (FAQ)

What is the integral of x^2(4-x) ?
The integral of x^2(4-x) is (4x^3)/3-(x^4)/4+C