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Popular Calculus >

integral of x^2(2-x)

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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