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Popular >

integral of x^2-y^2

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

limit as x approaches 2+of sqrt(x/(x-2))

x \to 2 + lim (\frac{x}{x - 2})

limit as x approaches 4 of 3x-1

x \to 4 lim (3 x - 1)

derivative of (5x/(7+x))

\frac{d}{d x} (\frac{5 x}{7 + x})

derivative of ((x^3-x))/(1+x^2)derivative of

\frac{( x ^{3} - x )}{1 + x ^{2}}

derivative of ((1+16t^2))/((4t)^3)derivative of

\frac{( 1 + 16 t ^{2} )}{( 4 t ) ^{3}}

Frequently Asked Questions (FAQ)

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