# exact length of the curve

Not what you're looking for? Search our solutions OR ask your own Custom question.

Find the exact length of the curve defined by y=2[(sqrt(x))^(3)]-1=2x^(3/2)-1 from x=0 to x=2. Set up the integral, use the substitution method( reverse chain rule), and express your answer in radical form. (ex sqrt(2), not 2.141).

Â© BrainMass Inc. brainmass.com December 24, 2021, 9:54 pm ad1c9bdddfhttps://brainmass.com/math/curves/exact-length-curve-423060

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Find the exact length of the curve defined by y=2[(sqrt(x))^(3)]-1=2x^(3/2)-1 from x=0 to x=2. Set up the integral, use the substitution method( reverse chain rule), and express your answer in radical form.

The length of the curve is calculated as:

So we first find the derivative of the function

Then the length of the curve from x = 0 to x = 2 is:

Let . Then,

Substitute x and dx to the above integral:

Now substitute x back to indefinite integral in terms of x.

So the length of the curve from x = 0 to x = 2 is:

Â© BrainMass Inc. brainmass.com December 24, 2021, 9:54 pm ad1c9bdddf>https://brainmass.com/math/curves/exact-length-curve-423060