Jump to content

Calculus question

Recommended Posts

Hi guys, I have a question on Calculus and it has two sub-questions. It would be great if any of you could help me solve this.

Sub-question 1, do I equate the equation to y equals something and then solve? And I have no idea on how to solve the second sub-question.

Screenshot_4.png

Share this post


Link to post
Share on other sites

sub q 1: know what formula to use for revolution around x axis (int of pi y^2 dx from x=a to x=b) and express y^2 in terms of x.

sub q 2: this is hl, it seems. use V around y-axis (int of pi x^2 dy from y=a to y=b) however note there is a large hole in the middle of the resulting solid. Give it a shot! Now that you know the formula, you should be able to derive the integral using intersection of graphs and inverse functions.

Edited by kw0573

Share this post


Link to post
Share on other sites
On 2017/4/22 at 0:41 AM, kw0573 said:

sub q 1: know what formula to use for revolution around x axis (int of pi y^2 dx from x=a to x=b) and express y^2 in terms of x.

sub q 2: this is hl, it seems. use V around y-axis (int of pi x^2 dy from y=a to y=b) however note there is a large hole in the middle of the resulting solid. Give it a shot! Now that you know the formula, you should be able to derive the integral using intersection of graphs and inverse functions.

This is what I got for sub 1:

int (x^2-9) dy

1/3 x^3 - 9x

and the answer if 110.

for sub 2, still don't know how to work out the hole in the middle, this is what I got so far:

int (9+y^2) dx - int sqrt(9+y^2) dx

I wonder what should I do next.

Share this post


Link to post
Share on other sites

1) Leave in exact form (n pi). I got a different answer, 44/3 pi, which is about 46.

2) This is HL. You need to integrate over dy (not dx), see formula i gave in previous response. May this diagram help

KEw5baX.jpg

 

 

Edited by kw0573

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

×