How to evaluate a double integral over a bounded region?

In summary, the conversation discusses the evaluation of a double integral over the region R bounded by y= 3x, 2x+ y= 5, x= 0, and y= 0. There appears to be a mistake in the problem, as the given answer is negative, but the integral cannot be negative in the first quadrant where x and y have only positive values.
  • #1
mduffy
3
0
how do I evaluate the double integral 2x + y dA over the region R bounded by y = 3x, 2X + y = 5, x = 0, and y = 0
 
Last edited:
Physics news on Phys.org
  • #2
mduffy said:
how do I evaluate the double integral 2x + y dA over the region R bounded by y = 3x, 2X = y = 5, x = 0, and y = 0

Check this entry ...
 
  • #3
skeeter said:
Check this entry ...
Thanks...should be 2x + y = 5
 
  • #4
over the region R bounded by y = 3x, 2X + y = 5, x = 0, and y = 0

Region R is bounded by either x = 0 or y = 0 ... how is it bounded by both axes and the two given lines?
 
  • #5
skeeter said:
Region R is bounded by either x = 0 or y = 0 ... how is it bounded by both axes and the two given lines?

Agreed! I think the teacher made a mistake with the problem. The given answer (no steps shown) is -2875/6. I am thinking there is an error in how the question is asked.
 
  • #6
The lines y= 3x and 2x+ y= 5 form one triangle with x= 0 and another with y= 0. But both of those are in the first quadrant where x and y have only positive values. The integral of (2x+ y) dA can't be negative over either of them.
 

1. What is a double integral?

A double integral is a type of mathematical integral that involves integrating a function over a two-dimensional region. It is represented by two sets of limits, one for each variable in the function.

2. Why is it useful to know how to solve a double integral?

Double integrals are commonly used in physics, engineering, and other fields to calculate volume, surface area, and other quantities. They also have applications in statistics and probability.

3. How do I solve a double integral?

To solve a double integral, you first need to identify the limits of integration for each variable. Then, you can use integration techniques such as Fubini's theorem or change of variables to solve the integral.

4. What are some common mistakes when solving a double integral?

Some common mistakes when solving a double integral include forgetting to change the limits of integration when using a change of variables, not considering the order of integration, and making calculation errors.

5. Are there any online resources or tools that can help with solving double integrals?

Yes, there are many online resources and tools available to help with solving double integrals. Some popular options include Wolfram Alpha, Symbolab, and Desmos. It is also helpful to consult textbooks or ask a math tutor for assistance.

Similar threads

I How to evaluate the enclosed area of this implicit curve?
    • Calculus
Replies
2
Views
2K
MHB How do I set up double integrals for different orders of integration?
    • Calculus
Replies
4
Views
1K
MHB 15.1.25 Evaluate the following double integral over the region R
    • Calculus
Replies
7
Views
2K
MHB Set Up Double Integrals....3
    • Calculus
Replies
5
Views
1K
MHB Can double integrals be interpreted as net change?
    • Calculus
Replies
1
Views
819
MHB Set Up Double Integrals....4
    • Calculus
Replies
10
Views
2K
MHB 8.2.2 Int area of a region and graph
    • Calculus
Replies
1
Views
693
B Why is this definite integral a single number?
    • Calculus
Replies
20
Views
2K
A Double integral with infinite limits
    • Calculus
Replies
11
Views
2K
MHB Evaluate the surface integral $\iint\limits_{\sum}f\cdot d\sigma$
    • Calculus
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top