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fk378
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Homework Statement
How do you solve the double integral of cos(u/v) dudv, if the limits of u are v and -v, and the limits of v are 1 and 2?
I tried doing it by parts but I didn't get it...
fk378 said:Homework Statement
How do you solve the double integral of cos(u/v) dudv, if the limits of u are v and -v, and the limits of v are 1 and 2?
I tried doing it by parts but I didn't get it...
fk378 said:If I integrate cos first and treat v as a constant, then I get v(sin(u/v))...isn't that messy? Can you show me what you did or explain it further please?
And I am using Stewart's calc, not glyn
To set up a double integral, you first need to determine the limits of integration for both variables, usually denoted as x and y. These limits are typically the boundaries of the region of integration. Then, you need to determine the integrand, which is the function that you are integrating over the region. Finally, you need to choose the order of integration, which determines which variable you integrate first.
A single integral is used to find the area under a curve in a one-dimensional space. A double integral, on the other hand, is used to find the volume under a surface in a two-dimensional space. Essentially, a single integral integrates over a line, while a double integral integrates over a region.
Evaluating a double integral involves using the fundamental theorem of calculus, which states that integration is the inverse of differentiation. This means that you can evaluate a double integral by first finding the antiderivative of the integrand, and then plugging in the limits of integration and subtracting the resulting values.
Double integrals are important in mathematics because they allow us to calculate the volume of three-dimensional objects, which is crucial in many fields such as physics, engineering, and economics. They also have applications in probability and statistics, where they are used to find the probability of events in a two-dimensional space.
Some common techniques for solving double integrals include using iterated integrals, where you integrate one variable at a time, and using change of variables, where you substitute new variables to simplify the integrand. Other techniques include using symmetry and using polar coordinates for circular or symmetric regions of integration.