# Integrating Intergration Problem: 1/x^3*sqrt(x^2-1)dx

• miller8605
In summary, integrating the function 1/x^3*sqrt(x^2-1)dx allows for the calculation of the area under the curve represented by the function, which is useful in various fields of science. The process involves using integration techniques to find an antiderivative, and the domain of the function is all real numbers except for x = ±1. This function cannot be solved using basic integration rules and has real-world applications in calculating work, volume, velocity, and economic quantities.
miller8605

## Homework Statement

i'm taking a defitinite integral from sqrt2 to 2 of the function 1/x^3*sqrt(x^2-1)dx.

## The Attempt at a Solution

I separated it into 1/x^3 and 1/sqrt(x^2-1). I have the second part using trig sub. as being inverse sec(x/1) dx. I believe i did this part correctly.

What I can't remember is that I make 1/x^3 to x^-3 and then integrate it that way with the final being -1/2(1/x^2)??

Why don't try the substitution u = x^2?

## 1. What is the purpose of integrating the function 1/x^3*sqrt(x^2-1)dx?

The purpose of integrating this function is to find the area under the curve represented by the function. This is useful in various fields of science, such as physics, engineering, and economics.

## 2. What is the process of integrating 1/x^3*sqrt(x^2-1)dx?

The process of integrating this function involves using integration techniques, such as substitution, integration by parts, or trigonometric substitution, to simplify the function and find an antiderivative, which represents the area under the curve.

## 3. What is the domain of the function 1/x^3*sqrt(x^2-1)dx?

The domain of this function is all real numbers except for x = ±1, as these values would result in a division by 0, which is undefined.

## 4. Can the function 1/x^3*sqrt(x^2-1)dx be solved using basic integration rules?

No, this function cannot be solved using basic integration rules, such as the power rule or the product rule. It requires more advanced integration techniques to find an antiderivative.

## 5. What are some real-world applications of integrating 1/x^3*sqrt(x^2-1)dx?

This function can be used to calculate the work done by a variable force, the volume of certain shapes, or the velocity of an object with a changing acceleration. It also has applications in economics, such as calculating the marginal cost or marginal revenue of a product.

• Calculus and Beyond Homework Help
Replies
10
Views
610
• Calculus and Beyond Homework Help
Replies
5
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
436
• Calculus and Beyond Homework Help
Replies
14
Views
508
• Calculus and Beyond Homework Help
Replies
22
Views
1K
• Calculus and Beyond Homework Help
Replies
2
Views
387
• Calculus and Beyond Homework Help
Replies
12
Views
1K
• Calculus and Beyond Homework Help
Replies
7
Views
823
• Calculus and Beyond Homework Help
Replies
9
Views
803
• Calculus and Beyond Homework Help
Replies
44
Views
4K