Is this correct? (+1 medal will be given)

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.
(x - 3) = (y − 7)$^2$, x = 19

A: $y = 7\pm \sqrt{(19)-3} = 3 or 11 $, therefore:
$$\huge\int\limits_3^{11} (2 \pi)(y)(3 + (y − 7)^2) dy = \frac{2800 \pi}{3} $$

Graph below:

Question

Is this correct?   (+1 medal will be given)

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.
(x - 3) = (y − 7)$^2$,  x = 19

A: $y = 7\pm \sqrt{(19)-3} = 3 or 11 $, therefore:
$$\huge\int\limits_3^{11} (2 \pi)(y)(3 + (y − 7)^2) dy = \frac{2800 \pi}{3} $$

Graph below:

anonymous · Answer

attachment

anonymous · Answer

I'm doing something wrong here I believe, because the computer is going NO! *slap*

anonymous · Answer

i don't see anything wrong...

anonymous · Answer

that is correct...

anonymous · Answer

Hmm, it's not taking the answer though.  (online homework thing, and I thought I had this section well understood)

anonymous · Answer

http://www.wolframalpha.com/input/?i=integrate+from+3+to+11+for+2pi+y+%283+%2B+%28y+%E2%88%92+7%29^2%29+dy

anonymous · Answer

Integration checks out, is it a setup error?

anonymous · Answer

Using the disk method is a non-option here I believe

anonymous · Answer

did you enter the decimal answer instead of the exact answer?

it is possible to do this using the disk (washer method) but not recommended... either way, the answer should still be the same..

anonymous · Answer

WebAssign (that's the the software provider is) allows for exact answer input (copy & paste disabled logically, but I can put it in as displayed above).

anonymous · Answer

I've double checked it and I've x = 3 + (y − 7)^2 and the rest of the instructions I've typed them over word for word.  I don't see any errors in my scratch work either

anonymous · Answer

all i can say is that there is nothing with your set-up or your integral...

anonymous · Answer

This is even one of those where you get to select the graph from multiple choice for points, and that's ok too.  So what the heck WebAssign?  :D

anonymous · Answer

write to them saying you got the answer correct but the computer won't accept it AND ask for monetary compensation since it's their fault and not yours...:)

anonymous · Answer

Correct ,give me my medal ...
JK,give it to Dpalnc

anonymous · Answer

HAHA!

anonymous · Answer

Maybe you all are right.  I mean integration isn't that hard on this problem, and even Wolf agrees so what the heck?  I tried entering it as a decimal and it slapped me down again.

anonymous · Answer

There's not some weirdness with a discontinuity of some kind here is there?

I'm giving you a cookie for your hard effort @dpalnc :D

kinggeorge · Answer

Sorry I've just been sitting here so long, but don't you need to include the $x=19$ in the part you're integrating as well?

kinggeorge · Answer

I believe you should instead be integrating $$\huge\int\limits_3^{11} (2 \pi)(y)(19-(3 + (y − 7)^2)) dy $$

anonymous · Answer

Hmm, let me try that and see...  :-)

anonymous · Answer

YOU DID IT!  :D

Way to go @KingGeorge !!!  (darn I gave out the medal earlier, I'd have given you 5 right now if I could)

Hmm, now let me see if I understand why...

Area between curves?  y=19 is the upper layer?

anonymous · Answer

Kind of odd how it's all turned sideways because of the switch between what is normally independent and dependent

anonymous · Answer

A(y) $\rightarrow$ Right - Left?

anonymous · Answer

@dpaInc @Eyad , he got it, FYI :-D

kinggeorge · Answer

It should be the right minus the left in your integrand for the shell method.