Area between two curves problem

[calculusisfun]

Homework Statement

(a) Find the area A, as a function of j, of the region in the 1st quadrant enclosed by the y-axis and the graphs of y = x ^ (1/3) and y = j for j > 0.

(b) What is the value of A when k = 2

(c) If the line y = k is moving upward at the rate of 1/2 units per second, at what rate is A changing when k = 2?



2. The attempt at a solution

Ok, so I doubt this is right as I was really, confused, but this is what I did...

(a)
x^(1/3) = j
x = j^3

A(j) = integral of (j - x^(1/3))dx from 0 to j^3

(b) A(2) = integral of (2 - x^(1/3))dx from 0 to 2^3
this equals = 4

(c) I have no idea..
I took the derivative of A(x) and got zero...

Please help. :)

 

[Quinzio]

You computed corretcly the Area, which is a function of ? (name it)

If j changes, and you have a certain function of j, how do you compute the change of f(j) ?