HI
So let curve C have equation y = 4x^(3/2)
--------
3
Let a > 2. The portion of C btwn the points (2, (4(sqrt 2)^2)/3) and (a,(4a^(3/2))/3) has length 49/3
Find the value of a
So if y = (4x^(3/2))/3 then dy/dx = 2x^(1/2)
Correct me anywhere you see a mistake!!
Then L = integral sign (S) a= 2 and b= a sq rt( 1 + (dy/dx)^2) dx
= S a=2 b=a sq rt (1 + 4x) dx
SO then I let u = 1 + 4x so du = 4 dx
so when x = 2 then u = 9 and when x = a then u = 1 + 4a
L = 4 S a= 9 and b=1+4a sq rt u du which is 4(2/3)u^(3/2) a= 9 b = 1+4a
but when I do the substitution I get 265/8 = sq rt ((1+4a)^3) and since this is not a easy equation to solve I don't know what a is
Any idea where I went wrong???
Thanks
Struggling calculus beginner