Solving double integrals

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In summary, the problem involves evaluating the function f(x,y,z) = g(√(x^2 + y^2 + z^2)) over the sphere x^2 + y^2 + z^2 = 9, where g(t) = t-5. The approach to solving this involves integrating the function r-5 over the sphere with a radius of 3.
  • #1

Homework Statement



f(x,y,z) = g(√(x^2 + y^2 + z^2))
g(t) = t-5
evaluate ∯ f(x,y,z)ds

where S is sphere x^2 + y^2 + z^2 = 9


Homework Equations





The Attempt at a Solution



i don't know how to go about it. can someone help me with this, how to approach this from start to end. i will solve it, but i need to know the steps in doing it.
 
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  • #2
hi myfunkymaths! :smile:

(have a square-root: √ and try using the X2 icon just above the Reply box :wink:)
myfunkymaths said:
f(x,y,z) = g(√(x^2 + y^2 + z^2))
g(t) = t-5
evaluate ∯ f(x,y,z)ds

where S is sphere x^2 + y^2 + z^2 = 9

uhh? isn't that just integrating r - 5 over the sphere r = 3 ? :confused:
 
  • #3
tiny-tim said:
hi myfunkymaths! :smile:

(have a square-root: √ and try using the X2 icon just above the Reply box :wink:)


uhh? isn't that just integrating r - 5 over the sphere r = 3 ? :confused:

so what function do i integrate twice? and with what bounds was it
 
  • #4
but it's constant!
 

What are double integrals?

Double integrals are mathematical tools used to calculate the area under a surface in two dimensions. They are an extension of single integrals, which are used to calculate the area under a curve in one dimension.

How do you solve double integrals?

To solve a double integral, you need to first set up the limits of integration for both the inner and outer integrals. Then, you evaluate the inner integral first, treating the outer integral as a constant. Finally, you integrate the result of the inner integral to solve the outer integral.

What are the different types of double integrals?

There are two types of double integrals: iterated integrals and double integrals over general regions. Iterated integrals are used when the limits of integration are constant values, while double integrals over general regions are used when the limits of integration are functions.

What is the purpose of using double integrals?

Double integrals are useful in many scientific and mathematical fields, including physics, engineering, and economics. They allow us to calculate the volume, mass, and other properties of objects and surfaces in two dimensions.

What are some common mistakes when solving double integrals?

Some common mistakes when solving double integrals include incorrectly setting up the limits of integration, forgetting to evaluate the inner integral first, and mixing up the order of integration. It is important to carefully check the limits and order of integration to avoid these errors.

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