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Well /sci/ i went full autistic and started studying integral calculus on my own; i can't do 3 things.
I managed to find alternate formulas of the revolution function surface C(x), being these two first formulas.
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Let C (x) : Surface area of a revolution volume
And l (x) the arc length of a function f (x)
Pic related:
The first formula explains itself. I WOULD LOVE to know how to simplify it.
The second one was a thing i got when I was trying to find out the formula. MY Queation is how do i operate with it?
THE third one is the formula the book gave to me. How do I find out this formula?
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You could simplify C(x) by expressing cosine using the tangent (Use identities tan=sin/cos and sin^2+cos^2=1).
You'll get something like sqrt(1/tan arctan(dx/dy)) and the trig funcs will disappear.
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>>8727188
How?
Please help a brainlet in needs.
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>>8728549
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>>8728587
Isn't the "dx" going to change with this variable change, and give me a sin arctan dy/dx dt with a sqrt or smth like that?
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>>8728616
There's no variable change, my pic is only a proof that, for any x, cos(arctan(x)) equals 1 over sqrt(1+x^2).
When applied to the first integral, as expected, gives you the third one (which is in itself a more general result from differential geometry).
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>>8728621
Woah, I understand those eq on a higher level now. Thanks bud.
Thread posts: 8
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Thread images: 5