Question

\[\int_0^{100} \sqrt{1+(f'(x))^2}dx\]Where \(f(x) = 75\left( e^{\dfrac{x}{150}} + e^{-\dfrac{x}{150}} \right)\)

Answer 1

\[\int_0^{100} \sqrt{1+(f'(x))^2}dx\]Where \(f(x) = 75\left( e^{\dfrac{x}{150}} + e^{-\dfrac{x}{150}} \right)\)

Just copying the original question, because OS doesn't show \(\LaTeX\) for me in the opening post. So it's easier to read.

Answer 2

First calculate f'(x) . Can you do that?

Answer 3

f(x) =.... ?
hint : hyperbolic functions.

Answer 4

I end up with \(\displaystyle\int_0^{100}\sqrt{e^{x/75}+ e^{-x/75}-2}\space dx\)

I don't know what to do next... Any idea?

I don't know hyperbolic functions well.

Answer 5

look for the definition of cosh x

Answer 6

http://en.wikipedia.org/wiki/Hyperbolic_function

Answer 7

this will greatly simplify your integral

Answer 8

Got to go... We can discuss later. Sorry!

Answer 9

It would go like this :

\(f'(x) = 75(e^{\cfrac{x}{150} }\times \cfrac{1}{150} - \cfrac{1}{150} \times e^{-\cfrac{x}{150}})\)

\(f'(x) = \cfrac{-1}{2} (e^{\cfrac{x}{150}} - e^{-\cfrac{x}{150}})\)

why don't put f'(x) = tan t

Answer 10

Go to go now. Sorry would look later.