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jk8985
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Find the double integral of (integral sign) (integral sign) ydA where D is the region bounded by (x+1)^2, x=y-y^3, x=-1, and y=-1
Chris L T521 said:Restricting Jameson's graph of the region (including the graph of $y=-1$) appropriately gives us the region we're integrating over:
[graph]xk2g00psbd[/graph]
To evaluate the double integral over this region, you need to decide whether or not you should treat this as a Type I or Type II region (I'll just say that one way is much easier than the other).
Do you think you can determine the appropriate limits of integration and the double integral(s) needed to evaluate your original integral over this region? (Smile)
jk8985 said:∫-1(lower limit) to 0 (upper limit) ∫(-1 (lower limit) to y−y^3 (upper limit)) y dxdy
plus
∫0 (lower limit) to 1 (upper limit) ∫(√(y)-1)) (lower limit) to (y−y^3) (upper limit) y dxdy
I did mine as two different double integrals. Is that okay?
Did I get the two sets of double integrals correct this time?
jk8985 said:I get a non-real result when doing from 0 to -1 :( for the second double integral. for the first set of double integrals i get 11/30
jk8985 said:awesome, exactly what I got when I did it.
If you could help me with this, it would be awesome :)
http://mathhelpboards.com/calculus-10/angle-between-two-planes-8180.html
A double integral is a mathematical concept that involves calculating the signed area between a two-dimensional region and a plane. It is represented by two nested integrals and is used to solve problems related to volume, mass, and moments of inertia.
To solve a double integral, you first need to identify the limits of integration for both the inner and outer integrals. Then, you need to evaluate the inner integral and substitute the result into the outer integral. Finally, you evaluate the outer integral to get the final answer.
A single integral calculates the area under a curve in one dimension, whereas a double integral calculates the signed area between a two-dimensional region and a plane. In other words, a single integral deals with one variable, whereas a double integral deals with two variables.
Double integrals have various applications in physics, engineering, economics, and other fields. Some common applications include calculating volumes of irregularly shaped objects, finding the center of mass of a two-dimensional object, and determining the total mass of an object with varying density.
Yes, there is a specific order to evaluate a double integral, known as the "order of integration." The inner integral is always evaluated first, and then the result is substituted into the outer integral. This order can be reversed, depending on the problem, but the inner integral is always evaluated first.