Double Integral (underneath a surface and above a square)

In summary, there was a mistake in the last two integrals of the solution provided. After factoring in the coefficients, one of the possible answers provided by the professor was obtained.
  • #1
letalea
8
0

Homework Statement



The volume underneath the surface z= y/ (1+xy) and above the square {(x,y)| 2≤x≤3 , 3≤
y≤ 4} is:

Homework Equations



Please see attachment.

The Attempt at a Solution



Please see attachment for solution.

My professor had provided us with 8 possible solutions (where only one is correct). However the answer I had produced did not match with any of the 8. Any insight to where/how I went wrong is greatly appreciated!

Thanks in Advance!
 

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  • #2
letalea said:

Homework Statement



The volume underneath the surface z= y/ (1+xy) and above the square {(x,y)| 2≤x≤3 , 3≤
y≤ 4} is:

Homework Equations



Please see attachment.

The Attempt at a Solution



Please see attachment for solution.

My professor had provided us with 8 possible solutions (where only one is correct). However the answer I had produced did not match with any of the 8. Any insight to where/how I went wrong is greatly appreciated!

Thanks in Advance!
Your solution looked good to me.

What were the eight choices given?

Added in Edit:

There is a mistake in doing each of the last two integrals.

You should have coefficients of 1/3 & 1/2 respectively.
 
Last edited:
  • #3
Could you explain this mistake to me? As I am not seeing how I come to get the coefficients.

But yes you are right, when you factor in the coefficients it does give me one of the possible answers the prof gave us!
 
  • #4
[itex]\displaystyle \int\ln(1+3y)dy[/itex]

Let u = 1+3y → du = 3 dy → [itex]\displaystyle dy=\frac{1}{3}du[/itex]

Can you take it from there?
 
  • #5
Yes, that makes perfect sense. Thank you!
 

1. What is a double integral?

A double integral is a type of integral that involves calculating the area underneath a surface and above a square in two dimensions. It is used to find the volume of a solid in three dimensions.

2. How is a double integral calculated?

To calculate a double integral, the given surface is divided into small rectangles, and the area of each rectangle is calculated. These areas are then summed up to find the total area underneath the surface and above the square.

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

A single integral calculates the area under a curve in one dimension, while a double integral calculates the area under a surface in two dimensions. A single integral has only one variable, while a double integral has two variables.

4. What is the purpose of a double integral?

The purpose of a double integral is to find the volume of a three-dimensional object by calculating the area underneath a surface and above a square in two dimensions. It is commonly used in physics, engineering, and other fields of science to solve problems involving volumes and areas of irregular shapes.

5. Are there any applications of double integrals in real life?

Yes, double integrals have many applications in real life. They are used in physics to calculate the mass and center of mass of a three-dimensional object, in engineering to find the volume and surface area of irregular shapes, and in economics to calculate the expected value of a function. They are also used in computer graphics and image processing to create three-dimensional models and render images.

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