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# Calculus question

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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.

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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

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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.

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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

Edited by kw0573

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