00:01
We're given a curve and we're asking the exact length.
00:05
The curve is given by the equation y equals 3 plus 1 half hyperbolic cosine of 2x with x in the interval 0 1.
00:26
With this equation, we have that y prime.
00:34
This is going to be 1 1 .5 times the derivative of hyperbolic cosine evaluated at 2x times 2, which is simply.
00:46
Derivative hyperbolic cosine evaluated at 2x.
00:50
Now recall that the derivative hyperbolic cosine is like the derivative of cosine, except for it's not negative hyperbolic sign.
01:01
It's going to be positive hyperbolic sign.
01:03
So we obtain positive hyperbolic sign of 2x.
01:14
And therefore, we have that 1 plus y prime squared is 1 plus hyperbolic sine squared of 2x, and we have that by hyperbolic trigonometric identities, this is the same as hyperbolic cosine squared of 2x...