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 8.5 Arc Length ( Rectification ) The method of finding the length of the arc of a curve is called the rectification. For arc length, the function and its derivative must both be continuous on the closed interval. If y = f (x) and f’ (x) are continuous on [ a, b ], then the arc length ( L ) of f (x) on [ a,b ] is given by Similarly for, x = f (y) and f’ (y) are continuous on [ a,b ], then the arc length (L) of f (y) on [ a,b ] is given by Example 29 Find the length of the arc of f (x) = x3/2 on [ 0, 5 ]. Solution : both are continuous on [ 0, 5 ]. then length of arc of Example 30 Find the length of the arc of the parabola y2 = 12x cut off by the Latus rectum. Solution : y2 = 12 x ® Parabola. Comparing with y2 = 4 ax, we see that 4 a = 12 \ a = 3 \ AS = SL = 6 \ co-ordinates of L are (3,6) Example 31 Find the length of the curve y2 = (2 x - 1 )3, cut off by the line x = 4. Solution : y2 = (2 x - 1 )3 is a curve (i) symmetrical about the x-axis (ii) not passing through (0,0) (iii) it cuts the x-axis, where y = 0 \ x = ˝ \ It's vertex is at ( ˝ , 0) (iv) It does not cut the y-axis as, taking x = 0 we get y = ± i (v) No asymptotes. (vi) (2x - 1)3 positive \ y2 ³ 0 \ x ³ ˝ \ The curve lies in only 1st and 4th quadrants Now Index 8.1 Introduction8.2 Area 8.3 Volumes 8.4 Mean Value 8.5 Arc Length(Rectification) Chapter 1
Further Distribution Is Strictly Prohibited.

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