Explore BrainMass

# exact length of the curve

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

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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).

https://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:

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!