Question about a double integral.

In summary, there was a discussion about the double integral xcosy being bounded by y=0, y=x^2, and x=1. The person was able to integrate most of the way but got stuck when asked to plug in x^2 into x^2. They eventually solved it after making a correction to their first integral. They also mentioned that they are willing to type out their work if the handwriting on the white board is illegible.
  • #1
DavidAp
44
0
The double integral xcosy is bounded by y=0, y=x^2, and x=1. I was able to integrate almost wholly through; however, toward the end I was unsure what to do when i was asked to plug in x^2 into x^2. What do I do?!

Here is an image of my work on the white board. Please, if my hand writing is illegible tell me and I would be more than happy to type it all out for you.
Thank you for taking the time to review my question.

2vjajrn.jpg
 
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  • #2
Here you go, you can remove that giant image via edit.
2vjajrn.jpg
 
  • #3
Thank You!

I solved it after a triple glance at the board! I knew something had to be wrong so I change my first integral to be 0 -> 1 and it worked! I'm just putting this out there because I don't know how to delete a thread, but thank you anyways forum!
 
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Related to Question about a double integral.

1. What is a double integral?

A double integral is a mathematical concept used in calculus to calculate the volume between a curved surface and a rectangular region on a coordinate plane. It involves integrating a function of two variables over a specific region.

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

A single integral involves integrating a function of one variable over an interval, while a double integral involves integrating a function of two variables over a region in a coordinate plane. The result of a single integral is a scalar, while the result of a double integral is a volume or area.

3. When would I use a double integral?

A double integral is commonly used in physics, engineering, and other scientific fields to calculate the volume or surface area of irregular shapes or curved surfaces. It is also used in probability and statistics to calculate joint probabilities and expected values.

4. How do I set up a double integral?

The setup of a double integral depends on the specific problem and the region of integration. Generally, the inner integral will have a limit that is a function of the outer integral variable, and the limits on the outer integral will correspond to the boundaries of the region of integration. It is important to carefully define the limits and variables before solving the integral.

5. What are some common techniques for solving double integrals?

Some common techniques for solving double integrals include using the properties of integrals, such as linearity and symmetry, and converting to polar or cylindrical coordinates to simplify the integrand. It is also helpful to visualize the region of integration and break the integral into smaller, more manageable parts.

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