# Find the value of the iterated integral

• MHB
• erikgelfat
In summary, the conversation is about showing progress when asking for help on MHB and a suggestion is given to change the order of integration.
erikgelfat

Format ±X/Y
± is if the value is positive or negative (Duh)
X is the numerator (e.g. 7)
Y is the denominator (e.g. 11)

the question:

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Hello and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

A suggestion- the integral of $f_x(x, y)$ with respect to x is f(x, y) so change the order of integration!

## What is an iterated integral?

An iterated integral is a type of integral that involves multiple variables and is used to find the volume of a solid bounded by multiple surfaces.

## How do you set up an iterated integral?

To set up an iterated integral, you first need to determine the limits of integration for each variable. These limits are typically determined by the bounds of the solid or region being integrated over. Then, you need to identify the order of integration, which determines the order in which the variables are integrated.

## What is the difference between a single and iterated integral?

A single integral is used to find the area under a curve, while an iterated integral is used to find the volume of a solid bounded by multiple surfaces. In a single integral, there is only one variable being integrated, while in an iterated integral there are multiple variables being integrated in a specific order.

## Can an iterated integral have more than two variables?

Yes, an iterated integral can have any number of variables, depending on the dimension of the solid or region being integrated over. However, the process of setting up and solving the integral becomes more complex as the number of variables increases.

## What are some real-world applications of iterated integrals?

Iterated integrals are used in many fields of science, such as physics, engineering, and economics. They are commonly used to find the center of mass of an object, calculate moments of inertia, and determine the volume of irregularly shaped objects. They are also used in probability and statistics to calculate probabilities and expected values.

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