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The Length of a Curve

Using the curve y=2x^(3/2) +3 (3/2 is the power on x) from x=0 to x=4 :
A.) estimate the length of the curve by computing the straight line distance between the endpoints.
*I found the answer to be sq root of 272 or approx. 16.4924. Sound correct?

B.) Compute exact length of the curve.
*I'm using S = The Integral from 0 to 4 sq root of 1 +(3x^1/2)^2 dx, but I get a huge number - what am I doing wrong?

Solution Summary

The length of a curve is calculated using an integral.