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Popular >

integral of y^2-x^2

Solution

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

Solution

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

Solution steps

\int y^{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 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

f(x)= 1/(x^2)+5 1/(x^3)

f (x) = \frac{1}{x ^{2}} + 5 \frac{1}{x ^{3}}

(\partial)/(\partial t)(te^t+2)

\frac{\partial}{\partial t} (t e^{t} + 2)

derivative of f(x)=sqrt(3x^2-5x+6)derivative of

f (x) = 3 x^{2} - 5 x + 6

derivative of (e^x^{cos(x)})

\frac{d}{d x} ((e^{x})^{c o s (x)})

d/(dz)(z^5-e^zln(z))

\frac{d}{d z} (z^{5} - e^{z} ln (z))

Frequently Asked Questions (FAQ)

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