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Popular Calculus >

integral of a^2-x^2

Solution

integral

a^{2} - x^{2}

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of (e^x)/((1+e^x))

in t e g r a l \frac{e ^{x}}{( 1 + e ^{x} )}

integral of 3/((2-x)^2)

in t e g r a l \frac{3}{( 2 - x ) ^{2}}

integral of 1/((x-2)^2)

in t e g r a l \frac{1}{( x - 2 ) ^{2}}

integral of (e^y)^3

in t e g r a l (e^{y})^{3}

integral of (sin^2(x))(cos^2(x))

in t e g r a l (sin^{2} (x)) (cos^{2} (x))

Frequently Asked Questions (FAQ)

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