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Popular Calculus >

integral of r^2-x^2

Solution

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

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

y^{''}+4y=sec(2x)

y^{^{''}} + 4 y = sec (2 x)

derivative of-(15/(16x^{7/2)})

\frac{d}{d x} (- \frac{15}{16 x ^{\frac{7}{2}}})

limit as x approaches 0 of (sin^3(x))/x

x \to 0 lim (\frac{sin ^{3} ( x )}{x})

derivative of (3x)/(sqrt(x^2+3))derivative of

\frac{3 x}{x ^{2} + 3}

y^{^{'}} = \frac{x}{3 y}

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