How would you describe the region R as a set? IOW, R = {(x, y) | <inequality involving x> and <inequality involving y>}.Math10 said:Homework Statement
Evaluate the double integral (x+2y)dA, where R is the region in the first quadrant bounded by the circle x^2+y^2=9.
Homework Equations
None.
The Attempt at a Solution
I know how to evaluate the double integral but I just don't know how to find the limits of integration. I know that the radius of the circle is 3.
That would be a square in the first quadrant.Math10 said:From 0 to 3?
Why would y be negative?Math10 said:So y=sqrt(9-x^2) and y= - sqrt(9-x^2)?
Yes. Now what are your limits for x?Math10 said:So y=0 to sqrt(9-x^2)?
You tell me ...Math10 said:dy dx?
A double integral is a mathematical concept used to find the volume under a surface or between two surfaces in three-dimensional space.
To evaluate a double integral, you first need to set up the limits of integration for both the inner and outer integrals. Then, you can use various integration techniques such as substitution, u-substitution, or integration by parts to solve the integral.
A single integral is used to find the area under a curve in one dimension, while a double integral is used to find the volume under a surface or between two surfaces in two dimensions.
Yes, certain calculators have the capability to evaluate double integrals using numerical methods such as Simpson's rule or the trapezoidal rule. However, it is important to note that these methods may not give exact solutions and may be subject to rounding errors.
Double integrals have various applications in physics, engineering, and economics. They are used to calculate the work done by a force, find the center of mass of an object, and determine the total profit of a business, among other things.