Solving Double Integrals: Sketch and Evaluate

  • Thread starter kieranl
  • Start date
  • Tags
    Integrals
In summary, a double integral is a mathematical tool used to calculate the volume under a surface in a two-dimensional space by integrating a function of two variables over a specific region in the coordinate plane. To sketch one, you identify the boundaries of the region and plot the curves defining them on a graph. Evaluating a double integral involves finding the antiderivative of the function and plugging in the boundaries. The boundaries are determined by the limits on the x and y axes, which can be found by solving equations defining the region. Some common applications of double integrals include calculating volume, surface area, joint probabilities, and expected values in various fields such as physics, engineering, economics, and statistics.
  • #1
kieranl
24
0
double integrals!

Homework Statement



sketch the region of integration then evaluate the double integral



Homework Equations



[tex]^{2}_{0}[/tex][tex]\int[/tex][tex]^{4}_{x^2}[/tex][tex]\int[/tex]xey2dydx


3. The Attempt at a Solution

I can't even see how to start this problem. I've tried integration by parts but got no where! can some one please give me a direction?
 
Physics news on Phys.org
  • #2


Try changing the order of integration, though I couldn't read what your bounds were =[.
 

What is a double integral?

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

How do you sketch a double integral?

To sketch a double integral, you first identify the boundaries of the region of integration. Then, you plot the curves that define these boundaries on a graph and shade in the region between them. This will give you a visual representation of the area over which the integral will be calculated.

What is the process for evaluating a double integral?

Evaluating a double integral involves finding the antiderivative of the function being integrated and then plugging in the boundaries of the region of integration. This will give you a numerical value that represents the volume under the surface.

How do you determine the boundaries of a double integral?

The boundaries of a double integral are determined by the limits on the x and y axes. These limits can be found by looking at the equations that define the region of integration and solving for the variables.

What are some common applications of double integrals?

Double integrals are commonly used in physics, engineering, and economics to calculate volume, surface area, and other important quantities. They are also used in probability and statistics to calculate joint probabilities and expected values.

Similar threads

Please evaluate this double integral over rectangular bounds
    • Calculus and Beyond Homework Help
Replies
10
Views
1K
Calculate this Integral around the Circular Path using Green's Theorem
    • Calculus and Beyond Homework Help
Replies
3
Views
237
Solve p = P(2X <= Y^2) using double integral
    • Calculus and Beyond Homework Help
Replies
4
Views
835
Double Integral Problem: Incorrect Jacobian Calculation for Polar Coordinates
    • Calculus and Beyond Homework Help
Replies
4
Views
890
Symmetry of an Integral of a Dot product
    • Calculus and Beyond Homework Help
Replies
9
Views
947
Reversing the order of integration in a double integral
    • Calculus and Beyond Homework Help
Replies
17
Views
2K
Double Integral via Appropriate Change of Variables
    • Calculus and Beyond Homework Help
Replies
3
Views
911
Complex Integration Along Given Path
    • Calculus and Beyond Homework Help
Replies
3
Views
852
Evaluate an integral over a triangle
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
Can a human calculate this without a calculator?
    • Calculus and Beyond Homework Help
Replies
11
Views
682

Hot Threads

Recent Insights

Back
Top