# Math 61

posted by .

Find the arc length of the curve y^3=8x^2 fr0m x=1 to x=8.

• Math 61 -

since y^3 = 8x^2,
y = 2x^(2/3)
y' = 4/3 x^(-1/3)
y'^2 = 16/(9x^(2/3))

arc length is thus
∫[1,8] √(1+16/(9x^(2/3))) dx

u=x^-2/3
then let v = u^1/2
then let 4w = 3tanv

and you finally wind up with

1/27 √(9+16/x^2/3) (9x + 16x^1/3) [1,8]
= 1/27 ((√(9+4)(72+32))-(√(16+9)(9+16)))
= 1/27 (104√13 - 125)

## Similar Questions

1. ### math

Whats the difference between an arc [of a circle]'s length and measure?
2. ### multivariable calc

Please help! Find the point where the curve r(t) = (12sint)i -(12cost)j +5k is at a distance 13pi units along the curve from the point (0,-12,0) in the direction opposite to the direction of increasing arc length. (Hint: ty -13pi for …

I'm desperate! Find the point where the curve r(t)=(12sint)i - 12(cost)j+ 5tk is at a distance 13pi units along the curve from the point (0,-12,0) in the direction opposite to the direction of increasing arc length. Thanks for any …
4. ### calc 3

find the arc length of the curve r(t)= <6sqrt(2),e^t,e^(-6t)>
5. ### Math rem

2.Find the length of the arc in a circle if the radius of the circle is 24cm and the degree of the arc is 90o 3.Find the length of the arc if a circle if the degree if the arc is 120o and the length of the radius is 8cm. 4. A circle …
6. ### Calculus

For the curve r = 2 sin 3(theta): Find the arc length of one petal
7. ### AP Calc B/C

Find the arc length of one arch of the sine curve. I started it by doing y=sinx, y'=cosx arc length= integral of sqrt(1+cos^2x)dx from pi/2 to 3pi/2 but I don't know how to integrate that! Thank you!
8. ### Math Arc Length

Find the arc length corresponding to an angle of a degrees on a circle radius of 4.9 Enter the exact answer. I put the arc length was 4.9api/180 got it wrong. Any help?
9. ### math

find the arc length of the curve y = lnx for x = 1 to x = square root of 8
10. ### apex geometry

Hannah constructed two similar circles as seen in the image below. If the arc length of the larger circle is , which of the following would be true?

More Similar Questions