7.4 Arc Length. I. Arc Length A.) Given the curve f (x), we can approximate the length from x = a to x = b by using the distance formula.

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7.4 Arc Length

I. Arc Length A.) Given the curve f (x), we can approximate the length from x = a to x = b by using the distance formula.

B.) The question is, can we get a closer approximation? The answer is YES! We can pick various points along the curve and calculate the linear distance between each pair. Summing these various lengths, gives us much closer approximation.

D.) Now if we take limit as the number of intervals gets infinitely large, we can find the exact arc length of any curve.

II. Examples A.) Ex. 1- Find the length, by hand, along the curve y = ½ x for 0 ≤ x ≤ 3.

B.) Ex. 2- Find the length, by hand, along the curve for 0 ≤ x ≤ 1.

C.) Ex. 3- Find the length, by TI-83, along the curve for -8 ≤ x ≤ 8.

Or, change to y…