Applications of Integration: Volumes Part II

Hckyplayer8 said:
I believe the closest example in my book (Stewart's Single Variable Calculus 7th edition) is as follows-

Page 358, Example 6

"Find the volume of the solid obtained by rotating the region in Example 4 about the line x = -1."

Example 4's problem was

"The region R enclosed by the curves y=x and y=x2 is rotated about the x-axis. Find the volume of the resulting solid"

Example 6's Solution

"Figure 11 shows a horizontal cross-section. It is a washer with inner radius 1+y and outer radius 1+ sqrt(y), so the cross-sectional area is
A(y) = (pi)[outer radius)2] - (pi)[(inner radius)2]

It then goes on to show the math and figure.

The figure has the line x = -1 drawn which I have replicated by drawing the line in my problem of x=2.

To account for the central axis shift from 0 to -1, the example problem adds 1 to the radii.

I followed that (first incorrectly by adding 2) by subtracting 2. This part I feel pretty confident I have right. Which means my error has to be related to the radii.
Click to expand...
In that example, the distance from x on the curve to the axis x = -1 is x - (-1) = x + 1, because x is to the right of -1.

In this problem, the distance from x on the curve to the axis x = 2 is 2 - x, because x is to the left of 2.

In general the distance from a to be is |a - b|, which is a - b if a is greater, and b - a if b is greater.
 
This subject is so infuriating. No doubt I've grown the most in this course compared to my previous three courses combined.

However when I hit a problem that I don't understand, boy do I suck.
 
Hckyplayer8 said:
This subject is so infuriating. No doubt I've grown the most in this course compared to my previous three courses combined.

However when I hit a problem that I don't understand, boy do I suck.
Click to expand...
It is great that you matured mathematically! Do you really think that calc 2 is harder than precalc?

You need to take a break from this material for a bit and come back at it refreshed.
 
Jomo said:
It is great that you matured mathematically! Do you really think that calc 2 is harder than precalc?

You need to take a break from this material for a bit and come back at it refreshed.
Click to expand...

I've read that Calc 2 is the hardest of the bunch/has the highest fail rate.

I agree. Although time and tide waits for no man.

I just have one more lesson and test to close out this course with a very achievable mid range B that would make a nice early Christmas present.
Then I could get some off time before I start a Physics class.
 
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