Consider the solid obtained by rotating the region bounded by the given curves about the line y=6.
y=3e^-x, y=3, x=4
Find the volume.Another question on Disk/Washers in Calculus?
Sketch the region! You have a horizontal line through y=3 beginning at 0 (solve 3=3e^-x). You have a vertical line through x=4 which intersects at (4, 3e^-4) and you have a line through y = 6.
Your shell is sitting on the y-axis radius (6-y), height x and thickness dy.
So your integral will be 2pi integral (6-y)x dy. This is difficult because you have to solve x in terms of y: ln function!
If you use disks you will have radius 6-y and thickness dx for x=0 to x=4. When you are done you will have to subtract the cylinder with radius (6-3) and height 4.
pi integral (6-3e^-x)^2 dx from 0 to 4. Expand makes it easier and integrate each term!
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