Double Integral Help: Solving for e^sin(x) over D

In summary, the double integral can be evaluated by switching the order of integration or integrating with respect to dy and the final answer is 1.718. Order of iteration does not matter in this case.
  • #1
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double integral help??

Homework Statement


Evaluate the double integral

| | e^sin(x) dA
over the region
D = {(x,y) | 0 ≤ x ≤ π/2, 0 ≤ y ≤ cosx} .

Homework Equations


The Attempt at a Solution


how would i do this? i know that dA = dy(dx) so the integral would be
|(0 ≤ x ≤ π/2) |(0 ≤ y ≤ cosx) (e^sin(x) dy) dx

would i have to switch the integration? so it would be dx(dy) instead? or could i just integrate it with respect to dy and say it is y*e^sin(x)?
 
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  • #2
Order of iteration in such a double integral does not matter.

Edit: you're in the right direction.
 
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  • #3
OK, then i guess the rest is easy. i did get y*e^sin(x) when i integrated with respect to dy and my final answer was e1 - e0 = 1.718
 

FAQ: Double Integral Help: Solving for e^sin(x) over D

What is a double integral?

A double integral is a type of mathematical operation that involves calculating the area under a two-dimensional curve or surface. It is a generalization of a single integral and is typically used in multivariable calculus.

What is the purpose of a double integral?

The purpose of a double integral is to find the area of a region bounded by a two-dimensional curve or surface. It can also be used to calculate the volume of a three-dimensional solid or the average value of a function over a given region.

How is a double integral calculated?

A double integral is calculated by first setting up the boundaries of the region to be integrated over, and then using a specific integration technique, such as the Riemann sum or iterated integrals, to evaluate the integral.

What are some common applications of double integrals?

Double integrals have many applications in physics, engineering, and economics. They can be used to calculate the mass of an object with varying density, determine the center of mass of a system, and find the work done by a variable force. They are also commonly used in statistics to calculate probabilities and expected values.

What are some tips for solving double integrals?

Some tips for solving double integrals include sketching the region of integration, choosing the appropriate limits of integration, and using symmetry to simplify the integral. It is also helpful to break down the integral into smaller parts and to use substitution or integration by parts when necessary.

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