The length of the graph of f(x) = 2/3x^(3/2) over [0,p] equals 52/3. Find p.
I think p is about 8.09.
y' = √x
∫[0,p] √(1+x) dx = 2/3 (1+x)^(3/2) [0,p]
= 2/3 (1+p)^(3/2) - 2/3 = 52/3
2/3 (1+p)^(3/2) = 18
√(1+p) = 3
1+p = 9
p = 8
Not sure why you resorted to decimals, when fractions are exact.