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Popular Calculus >

integral of y^2+x^2

Solution

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

Solution

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

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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