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We begin with the curve with equation y = x2 and try to approximate arc length of the curve from (0,0) to (1,1). The easiest
We begin with the curve with equation y = x2 and try to approximate arc length of the curve from (0,0) to (1,1). The easiest possible approximation is to simply use a straight line from (0, 0) to (1, 1). What is the length of the line segment joining the points (0,0) and (1,1)? We will call this the N = 1 approximation since we used a single line segment to approximate the arc length. (If you don't know how to find this length, make it the hypotenuse of a right triangle and then use the Pythagorean Theorem.)
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