00:01
We're given a curve and we're asked to find the exact length of this curve.
00:05
The curve has equation y equals x cubed over 3 plus 1 over 4x, where x lies in the interval 1, 2.
00:25
Therefore, we have that the derivative of y with respect to x, y prime, is equal to x squared, and then minus 1 over 4x squared.
00:44
And therefore, 1 plus y prime squared is equal to 1 plus, and then we have x to the 4th minus 2 times x squared times 1 4th, 1 over x squared.
01:17
So the x squared to cancel out, and then we get minus one -half, and plus one -sixteenth, x -to -the -fourth, or, yeah, plus 1 over 16x to the fourth.
01:35
And so we get x -to -the -fourth plus one -half, plus one -sixteenth, x -to -the -fourth, which can be factored as x -squared plus 1 over 4x squared.
02:01
Squared...