Question

integration of x upon X square + Y square

Answer 1

Integration can be used to find the areas, volumes, central points and many useful things. But it is often used to find the area underneath the graph of the given function.
Integration is usually opposite to that of differentiation. Given function is x² + y²
and we have to integrate it with respect to x.
Now we know that the integration of a function x with respect to x is
∫ x dx = x² / 2 + C
what we have done here is that, we have raised the power of x by 1 and divide the function x with the same number as that of the power.
Let,
f(x) = x² + y²
Integrating with respect to x, we get:
∫ f(x) dx = ∫ (x² + y²) dx
∫ f(x) dx = ∫ x² dx + ∫ y² dx
∫ f(x) dx =  ∫ x² dx + y² . ∫ 1 dx
∫ f(x) dx = x²⁺¹ / (2+1) + y² . x / 1 + C
where C is any arbitrary constant.
∫ f(x) dx = x³ / 3 + x y² + C
Which is the answer.
Hope it helps you. Thanks.

Answer 2

The integration of x upon $x^2+y^2$  is $x^3/3+xy^2+C$.

Given:

$x^2+y^2$

To find:

To find intergration of x upon $x^2+y^2$.

Solution:

Let $f(x) = x^2 + y^2$

Integrating with respect to x, we get:

∫ $f(x)dx=$∫ $(x^2+y^2)dx$

∫ $f(x)dx$ = ∫ $x^2 dx$ + ∫ $y^2 dx$

∫ $f(x) dx$ = ∫ $x^2 dx$ + $y^2.$∫ $1 dx$

∫ $f(x ) dx$ = ∫ $x^2 dx$ + $y^2 .\frac{x}{1}+C$

∫ $f(x) dx$ = $\frac{x^3}{3}+xy^2+C$

where C is any arbitrary constant.

Therefore, the integration of x upon $x^2+y^2$ is $x^3/3+xy^2+C$.

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