6) Find the length of the curve

I try many different way but I cant seem to find the rite answer! :( can you tell me the answer?

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- Apr 28th 2010, 08:57 PMnhatieFind the length of the curve
6) Find the length of the curve

I try many different way but I cant seem to find the rite answer! :( can you tell me the answer? - Apr 29th 2010, 04:11 AMmr fantastic
- Apr 29th 2010, 05:42 AMnhatie
then 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? - Apr 29th 2010, 08:16 AMHallsofIvy
This is wrong. the derivative of is so the derivative of is and the derivative of is

Similarly, the derivative of is .

Quote:

then 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! - Apr 29th 2010, 10:21 AMnhatie
i have sqrt (4y^1/3 + 1/16 y^1/3)^2 => int -343 to 512 (4y^1/3 + 1/16 y^1/3)

then

65/16y^1/3 |from -343 to 512

(65/16 (-343)^1/3) - (65/16 (512)^1/3)

is it the anwer?