This is wrong. the derivative of is so the derivative of is and the derivative of is
Similarly, the derivative of is .
Where in the world did the " " come from? You are calculating the arc-length of a path, not rotating anything around an axis! You seem to be grabbing formulas at random. The arclength of f(y), from y= a to b isthen i have 2pi int from -343 to 512 [(3)(y^4/3) - (3/32)(y^2/3)][sqrt[ 9( y^1/3)- (-9/32)(y^-1/3)] ???
I am not sure what I am doing... can you show me how to solve and the right answer?
Now, with , .
Notice that adding 1 to that just changes the "- 1/2" to "-1/2". And since that was a "perfect square" so is this: If x and y are such that 2xy= 1/2, then and then .
In other words, is also a perfect square and so we can get rid of the square root!