I am working on my last surface area problem, and am kind of hung up on the following:
Wait... could that be re-written as?:
That doesn't really help either...
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Is it ?
If so, this integral is unelementary.
Do you mean ?
The easiest way is the following identity... (1)
It is in fact which I have written as
Where is the identity derived from?
Its a well-known identity.
You can prove it by using the definitions of the Heperbolic Functions.
Another way to do it:
and it is easy to integrate.
Would that be the double angle formula for
Pardon my ignorance, but are all of the trig identities applicable to the hyperbolic functions?
No. Not all of them.
Also, sometimes there is a small difference like the signs.
Just to check my work...
What is the surface area of for when revolved about the x-axis?
Is this a reasonable looking answer?
Originally Posted by MechEng Would that be the double angle formula for
Pardon my ignorance, but are all of the trig identities applicable to the hyperbolic functions? Actually, yes, with some slight modifications. Have a look at Hyperbolic function - Wikipedia, the free encyclopedia, and look for "Osborn's Rule".
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