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Popular Calculus >

integral of-x^2+10x

Solution

\int - x^{2} + 10 x d x

Solution

- \frac{x ^{3}}{3} + 5 x^{2} + C

Solution steps

\int - x^{2} + 10 x 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^{2} d x + \int 10 x d x

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

\int 10 x d x = 5 x^{2}

= - \frac{x ^{3}}{3} + 5 x^{2}

Add a constant to the solution

= - \frac{x ^{3}}{3} + 5 x^{2} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of-x^2+10x ?
The integral of-x^2+10x is -(x^3)/3+5x^2+C