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# Maths C4 Integration clarification

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1. Could you clarify what exactly does the mark scheme mean by the bit highlighted
in red in this picture: [Its mainly the part ( 2-(part a answer) ) that I don't get why is it 2 - a when shouldn't it just be just the 'part a' value = 2- 1/ln(3) ] right click and open in new tab to zoom in btw

This is what I did and then stopped because I didn't really know how to subtract my 2 integration answers and noticed the mark scheme final answer would have been different so I'm curious as to why I have gone wrong and would appreciate if you would help me understand why as its the only question in 5+ past papers that has me on my mistake.

2. (Original post by XxKingSniprxX)
...
The cone you're interested in is formed by the rotation of the tangent line about the x-axis.
This tangent line, for the part of it you are interested in has values from to .
Hence you subtract the smaller value from the larger to establish the height of the cone.
3. (Original post by XxKingSniprxX)
...
Just integrating gets you the volume formed by rotating the curve between the portion x=0 to x=2, i.e: even the excluded bit under the line. You want to remove the volume formed by rotating the section under the line from x=1/ln 3 to x=2.

Rotating the region under the line (i.e: the portion between Q and P) forms a cone with height as the difference between the x coordinates of Q and P.
4. (Original post by joostan)
The cone you're interested in is formed by the rotation of the tangent line about the x-axis.
This tangent line, for the part of it you are interested in has values from to .
Hence you subtract the smaller value from the larger to establish the height of the cone.
(Original post by Zacken)
Just integrating gets you the volume formed by rotating the curve between the portion x=0 to x=2, i.e: even the excluded bit under the line. You want to remove the volume formed by rotating the section under the line from x=1/ln 3 to x=2.

Rotating the region under the line (i.e: the portion between Q and P) forms a cone with height as the difference between the x coordinates of Q and P.
So basically, I was supposed to do the height = x value of P-Q instead of the x value of Q - zero?

I should have really annotated the diagram to have seen that a bit clearer
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