Surely it's because you're told in the first line of the problem what the values of are...
I'm having some trouble with a question, I've got a lot of the difficult stuff down but I can't get the limits right and my answer is twice what it should be.
So I know that and that .Curve C:
The curve C is rotated through 360 degrees about the x-axis. Show that the curved surface area of the solid of revolution generated by:
Hence find this curved surface area.
So I have the right integral but I can't show that the limits are 0 to .
I don't think it wants me to use symmetry as that would make it , I tried but I can't get the right answers.
To be picky, it actually says show that the integral between those two points gives the surface area.
Could you perhaps, live up to your name of "prove it" and show me why the limits have to be what it says, as to me, mathematically they can't be.
I have just noticed that you have made a mistake in your integral. It appears you took out as a factor, but also left inside the integral as well. That will explain why you're getting double the answer you're supposed to.
It always helps to have a picture of what you are trying to do. In this case, to draw a graph of the function will mean you need to write in terms of , and the required range of will be the distance between intercepts.
If and , then
The intercepts are where , so
And since , solving will give and , but you can now use symmetry, since we have found why your answer is double what it should be.
Sorry I've gone over it again and I made a typo in my original post but the answer is still what I said it was:
So lower limit should be
And upper limit
So shouldn't it be:
So still, using symmetry would make it which is wrong.
I keep checking it and can't see where I'm wrong :S