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c3 Volumes of revolution question I don't understand. Help

Question 1:
curve y=x^2 +1. Rotated round the y axis and bounded by the y axis and the line y=4.

I assumed this meant between y=0 and y=4.

I keep on getting 4 pie for the answer but in the back of the book the answer is:4.5pie. Dont understand how they got this and Im getting all other revolution questions right with my method.

Question 2:
Curve:
x= e^y +1 rotated round y axis between y= 0 and y=ln2
I get answer 5 pie. Book has answer 7/2pie + pie ln2.

Help please.

Reply 1

nuodai

Question 1
If you draw a sketch of the graph of

y=x^2+1

then you'll notice that it intersects the y-axis at

y=1

and not

y=0

, so your integration limits should be

1 \le y \le 4

rather than

0 \le y \le 4

.

Question 2
Show your working; I agree with the book's answer.

(P.S. this is pi:

\pi

, and this is pie: click.)

Reply 2

steve2005

Original post by Yasin-Ali

Question 1:
curve y=x^2 +1. Rotated round the y axis and bounded by the y axis and the line y=4.

I assumed this meant between y=0 and y=4.
.

It seems odd to be bounded by y axis. Does the question actually say that
?

Reply 3

nuodai

Original post by steve2005

It seems odd to be bounded by y axis. Does the question actually say that
?

It seems normal to me; after all, it's being rotated about the y-axis.

Reply 4

JonathanM

What exam board is this?

Reply 5

f1mad

Gotta be careful here; as Nuodai pointed out.

I always tend to draw sketches for these types of questions, incase they niggle a sneaky trick in there (don't just assume the integral).

Reply 6

raheem94

Original post by steve2005

It seems odd to be bounded by y axis. Does the question actually say that
?

Its not very odd.

In edexcel they only give questions involving rotations of 360deg on the x-axis, but a few questions in the book do have the y-axis rotation questions and it is mentioned that such questions won't come up in the exam.

Reply 7

steve2005

Original post by raheem94

Since the rotation is about the y axis, it does not make sense to say it is bounded by the y axis.

I have done the question and it's easy never-the-less I'm 99.9% certain there is something wrong with the way the OP has given the question.

Reply 8

f1mad

Original post by steve2005

Hmm, I think the wording is fine.

Although I suspect, the OP should also say the region is bounded by the curve too.

Reply 9

steve2005

Original post by f1mad

Hmm, I think the wording is fine.

Although I suspect, the OP should also say the region is bounded by the curve too.

It is not bounded by the y axis. Sketch and you will see.

Reply 10

raheem94

Original post by steve2005

The OP has not written down the exact question.

If he would have written down the exact question then the question would have probably said that it is rotated by 360(or 2 pi).

(edited 11 years ago)

Reply 11

f1mad

Original post by steve2005

It is not bounded by the y axis. Sketch and you will see.

It is.

The question should read: the region bounded by the y axis, the line y=4 and the curve y= x^2+1.

Then there's a distinct region that is clearly bounded by all 3 restrictions.

Reply 12

steve2005

Original post by f1mad

It is.

The question should read: the region bounded by the y axis, the line y=4 and the curve y= x^2+1.

Then there's a distinct region that is clearly bounded by all 3 restrictions.