How about noting this about your function:
and is thus just a translated hyperbolic cosine, so the curve is a catenary. That might make the integral easier using hyperbolic function identities, but I can't say for sure.
--Kevin C.
Hi, am doing a question looking for the length of a curve, the function given is , from is my interval.
I got all the parts down i got then from the length of curve formula,
my problem is the integral under the square root, i tried substitution i tried parts i couldnt get anything, any clues on how to start off this integral. Thank You
How about noting this about your function:
and is thus just a translated hyperbolic cosine, so the curve is a catenary. That might make the integral easier using hyperbolic function identities, but I can't say for sure.
--Kevin C.
In fact, it will make the integral easier. With , we find , and so , and since , , so
, as the hyperbolic cosine is always positive, and you should be able to integrate that.
--Kevin C.