00:01
In this problem we are provided with the curve which is given by the parametric equations x equals to 2 times natural log of t and y equals to 9 times t plus 1.
00:14
We are asked to set up an integral to find out the arc length of this curve when 3 is less than or equal to t is less than or equal to 9.
00:26
So for this let us recall the formula for the arc length.
00:30
The arc length l equals to integral a to b square root of d x over dt the whole squared plus d, d .y over dt the whole squared dt.
00:48
So let us consider x.
00:50
We have x equals to two times natural log of t.
00:54
Now differentiating this with respect to t, we have two times the derivative of natural log of t is 1 over t.
01:01
So we have 2 over t.
01:04
Now let us square on both sides.
01:06
We have d x over d t the whole squared to be equal to 2 squared which is 4 over t squared.
01:14
And next let us consider y...