Chapter 8.4, Problem 6E

6a) Let A be the parabolic arc defined by the equation y = 8x – x over the domain interval [0, 8]. Sketch A on a set of coordinate axes below; identify the coordinates of both intercepts and the vertex. Estimate the length of A using the lengths of the two line segments joining either intercept to the vertex. Write the definite integral that represents the exact length of A. Do not evaluate this integral - just set it up and simplify it. Then, use technology to obtain an estimate of this integral's value. (report it correct to the thousandths place) b)

3) Find the equation of the curve whose arclength from the point (4, 1) to the point (9, -1) is given by the integral below. $2 x+1 x dx

Find the length of a curve