Find the following integral where f(x,y) = x^2 + y^2 + 3.


Find the following integral where {eq}f(x,y) = x^2 + y^2 + 3. {/eq}

In Several Variables:

When we calculate the integral of a function of several variables with respect to one variable, only that variable is considered as "variable", the rest of the variables operate as constant values in the process of calculating the integral.

Answer and Explanation:

Given the function {eq}f(x,y) = x^2 + y^2 + 3 {/eq}, we can calculate two kinds of integral, respect to one variable and respect to the other:

{eq}\int {\left( {{x^2} + {y^2} + 3} \right)} dx = \frac{{{x^3}}}{3} + x{y^2} + 3x + C\left( y \right)\\ \int {\left( {{x^2} + {y^2} + 3} \right)} dy = {x^2}y + \frac{{{y^3}}}{3} + 3y + D\left( x \right) {/eq}

Learn more about this topic:

Indefinite Integrals as Anti Derivatives

from Math 104: Calculus

Chapter 12 / Lesson 11

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