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Popular Calculus >

integral of r^2-x^2

Solution

integral

r^{2} - x^{2}

Solution

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

Solution steps

\int r^{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 r^{2} d x - \int x^{2} d x

\int r^{2} d x = r^{2} x

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

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

Add a constant to the solution

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

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

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