You are Here: Home >< Maths

P5 Surface Area q watch

1. The part of the curve y=x^2 between y=0 and y=2 is rotated completely about the y-axis. show that the area of the curved surface formed is 13pie/3

I am ok if it goes round the x-axis but what happens when its round the y-axis? can anybody help me out please?
2. (Original post by Mr_Joe_T)
The part of the curve y=x^2 between y=0 and y=2 is rotated completely about the y-axis. show that the area of the curved surface formed is 13pie/3

I am ok if it goes round the x-axis but what happens when its round the y-axis? can anybody help me out please?
3. (Original post by Gaz031)

If you need trouble evaluating the integral then post back.
Shouldn't the limits Xa and Xb be Ya and Yb ?
Or am i wrong?
4. ye they should be
5. (Original post by Syncman)
ye they should be
oh good....i just had a minor panic that i'd learnt it wrong!
6. How would you integrate that?
Substitution of y=1/4 sinh²u?
7. I got dy/dx as 1/(2√y)

then got it as 2pi∫(√y√((4y+1)/4y)
=(2/3)pi(4y+1)^3/2

which between limits gives an area of (18-2/3)pi=52pi/3

what did i do wrong :/
8. (Original post by lgs98jonee)
I got dy/dx as 1/(2√y)

then got it as 2pi∫(√y√((4y+1)/4y)
=(2/3)pi(4y+1)^3/2

which between limits gives an area of (18-2/3)pi=52pi/3

what did i do wrong :/
I edited my post.
10. (Original post by Lucky Penny)
yeah. which part u stuck on?
11. (Original post by majikthise)
How would you integrate that?
Substitution of y=1/4 sinh²u?
Nope!
you end up with,

Sa =2π ∫√y√(1+1/(4y) dy
= 2π ∫ √(y + ¼) dy
= 2π ∫ (y + ¼)^½ dy
= 2π(2/3)(y + ¼)^(3/2) [ 0 -> 4]
= 2π (2/3){(9/4)^(3/2) - (1/4)^(3/2)}
= 2π (2/3){(3/2)^3 - (1/2)^3}
= 2π (2/3){27/8 - 1/8}
= (4π/3){26/8}
= 13π/3
=====

Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 19, 2005
The home of Results and Clearing

2,253

people online now

1,567,000

students helped last year
Today on TSR

University open days

1. SAE Institute
Animation, Audio, Film, Games, Music, Business, Web Further education
Thu, 16 Aug '18
2. Bournemouth University
Fri, 17 Aug '18
3. University of Bolton
Fri, 17 Aug '18
Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants