Help with understand double integral solution?

In summary, the conversation discusses the formula for integrating (ax+b)^n using the formula (1/a(n+1))(ax+b)^n+1+C. The bottom denominators of -4 were obtained using the values of n=-2 and a=4. The formula does not need to be memorized, but it is important to know how to derive it.
  • #1
Chandasouk
165
0
http://img844.imageshack.us/img844/3293/17693169.jpg [Broken]

I follow it up to the third step, but how did they get the bottom denominators of -4? shouldn't it be -1?
 
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  • #2
∫(ax+b)ndx = (1/a(n+1))(ax+b)n+1+C

In their case, n=-2 and a=4
 
  • #3
Oh, should I know that formula or do most people look that up in a table? Been a while since I did Calc 2.
 
  • #4
Chandasouk said:
Oh, should I know that formula or do most people look that up in a table? Been a while since I did Calc 2.
You don't need to know that formula, but you should know how to derive it. rockfreak.667 used a very simple substitution to get it.
 

1. What is a double integral?

A double integral is a mathematical tool used to find the volume under a surface in three-dimensional space. It involves integrating a function of two variables over a two-dimensional region.

2. How do I solve a double integral?

To solve a double integral, you first need to set up the limits of integration by determining the boundaries of the region and choosing the order of integration. Then, you can evaluate the integral using integration rules and techniques such as u-substitution, integration by parts, or trigonometric substitution.

3. What is the difference between a single and a double integral?

A single integral involves integrating a function over a one-dimensional interval, while a double integral involves integrating a function over a two-dimensional region. A double integral can be thought of as stacking multiple single integrals on top of each other.

4. When would I use a double integral?

A double integral is often used in physics and engineering to calculate the volume or surface area of a three-dimensional object. It is also used in economics and statistics to find the total utility or probability of a two-variable system.

5. Can a double integral have more than two variables?

No, a double integral can only have two variables. It is a way to integrate a function of two variables over a two-dimensional region. However, multiple double integrals can be nested within each other to integrate functions of more than two variables.

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