MHB Volume of Solid of Revolution; Simpson's Rule

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The discussion focuses on calculating the volume of a solid generated by revolving the region bounded by the curve y=sqrt(x) and the lines y=1 and x=4 around the line y=1. Participants inquire about visualizing the region and the rotation process to better understand the solid's shape. Additionally, the conversation shifts to approximating the integral from 0 to 1 of 1/(1-x)^2 using Simpson's Rule with n=4. Questions arise regarding the setup and application of Simpson's Rule for this integral. The thread highlights the importance of both visualization and numerical methods in solving these calculus problems.
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1.find tthe volume solid generated by revolving the region bounded y=sqrt x and the ;lines y=1, x=4 about the line y=1

2. using simpson rule witj n=4 to aproximate int from 0 to 1 1 over 1-x power 2 dx
 
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1. Can you draw a picture of the region? Can you visualize how the region is being rotated?

2. So you're approximating $\displaystyle \int_0^1 \frac{dx}{(1-x)^2}?$ Is that correct? If so, how do you set up a Simpson's Rule?
 
Thread 'Problem with calculating projections of curl using rotation of contour'

Thread 'Problem with calculating projections of curl using rotation of contour'

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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