# Extremely different integral problem

• calculusisfun
In summary, an extremely different integral problem is a mathematical problem that involves finding the area under a curve or the volume of a solid in a way that is not typically taught in introductory calculus courses. These problems often require advanced techniques and creative thinking to solve. They can be considered extremely different if they do not fit into the standard categories of integration, and scientists may encounter them when trying to model complex systems or phenomena. Some common challenges when solving these problems include identifying the appropriate method of integration, dealing with complex functions or boundaries, and ensuring accuracy. Tips for tackling extremely different integral problems include breaking down the problem, using substitution or integration by parts, and having a strong foundation in calculus.
calculusisfun

## Homework Statement

(a) Find the area A, as a function of j, of the region in the 1st quadrant enclosed by the y-axis and the graphs of y = x ^ (1/3) and y = j for j > 0.

2. The attempt at a solution

(a)
x^(1/3) = j
x = j^3

A(j) = integral of (j - x^(1/3))dx from 0 to j^3

Any help would be much appreciated! :)

Thanks

I'd begin by writing down the equation of the Area, so that I can plug in the parameter j and get a number which is the Area.

Just do it, then...

## What is an "extremely different integral problem"?

An extremely different integral problem refers to a mathematical problem that involves finding the area under a curve or a volume of a solid in a way that is not typically taught in introductory calculus courses. These problems often require advanced techniques and creative thinking to solve.

## What makes an integral problem "extremely different"?

An integral problem can be considered extremely different if it does not fit into the standard categories of integration, such as finding the area under a curve or the volume of a solid of revolution. These problems often involve unconventional functions, boundaries, or methods of integration.

## How do scientists encounter "extremely different integral problems" in their research?

Scientists may encounter extremely different integral problems in their research when trying to model complex systems or phenomena. These problems may arise in physics, engineering, biology, economics, or other fields where precise calculations are necessary.

## What are some common challenges when solving "extremely different integral problems"?

Some common challenges when solving extremely different integral problems include identifying the appropriate method of integration, dealing with complex functions or boundaries, and ensuring the accuracy of the solution. These problems may also require a deep understanding of mathematical concepts and techniques.

## Are there any tips for tackling "extremely different integral problems"?

Yes, some tips for tackling extremely different integral problems include breaking down the problem into smaller, more manageable parts, using substitution or integration by parts to simplify the problem, and checking your solution for accuracy. It is also helpful to have a strong foundation in calculus and to be open to creative and unconventional approaches to problem-solving.

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