MHB Solving Double Integrals: Order of Integration Explained

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To solve the double integral by changing the order of integration, it is essential to sketch the region of integration first. This visualization helps in determining the correct bounds for the new order. The discussion suggests that the integral in question may be $$\int_{-3}^1\int_{2x}^{3-x^2}xy\,dy\,dx$$. By using horizontal strips instead of vertical ones, one can accurately set the new limits for integration. Understanding this process is crucial for successfully computing the solution.
Estelle
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Hey guys,

need your help and hope someone takes the time:

I need to solve the double integral by changing the order of Integration.

View attachment 4966

I would really appreciate if you could illustrate the way of how to compute the solution.

Best
Estelle :)
 

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Hello and welcome to MHB, Estelle! :D

I have moved this thread, since it is a problem more likely found in the 3rd semester of an elementary calculus course.

Are you certain the problem isn't actually:

$$\int_{-3}^1\int_{2x}^{3-x^2}xy\,dy\,dx$$?
 
Assuming that what Mark has posted is correct, to reverse the order of integration you need to SKETCH the region of integration, and then figure out your bounds by using horizontal strips instead of vertical ones...
 
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Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1## ##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0## I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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