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Popular Calculus >

integral of x^2(x-7)

Solution

\int x^{2} (x - 7) d x

Solution

\frac{x ^{4}}{4} - \frac{7 x ^{3}}{3} + C

Solution steps

\int x^{2} (x - 7) d x

Expand

x^{2} (x - 7) : x^{3} - 7 x^{2}

= \int x^{3} - 7 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 7 x^{2} d x

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

\int 7 x^{2} d x = \frac{7 x ^{3}}{3}

= \frac{x ^{4}}{4} - \frac{7 x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{7 x ^{3}}{3} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of x^2(x-7) ?
The integral of x^2(x-7) is (x^4)/4-(7x^3)/3+C