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Popular >

integral of x^2(x-2)

Solution

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

Solution

\frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} + C

Solution steps

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

Expand

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

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

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

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

= \frac{x ^{4}}{4} - \frac{2 x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} + C

Popular Examples

sum from n=0 to infinity of (n!)/(103^n)

n = 0 \sum \infty \frac{n !}{10 3 ^{n}}

(\partial)/(\partial y)(x^2+2xy^2+2y^2)

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

derivative of f(x)=x^3-3/2 x^2 derivative of

f (x) = x^{3} - \frac{3}{2} x^{2}

area y=2-|x|,y=x^2 area

y = 2 - ∣ x ∣, y = x^{2}

derivative of 1/x+6 derivative of

\frac{1}{x} + 6

Frequently Asked Questions (FAQ)

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