v. The cauchy’s principal of the improper integrals ( ) f x dx when a b f(x) has a singularity at c where a c b ≤ ≤ Further reading 1. Advanced Calculus By Watson Fulks John and sons New York. Brisbane Toronto. 94 CHAPTER 10 Length of an Arc of a Curve 10.1 Introduction If you ask a secondary school student to measure the length of an arc of a curve, he will use a string or a flexible material like a string placed upon the arc of the curve and he measures the length of the string placing against a ruler. Also an approximation of length could be found by marking a number of points on the arc and finding the sum of the lengths of all the chords that are small. Any mathematician could do the same method unless he knows the equation of the curve either in Cartesian form or Parametric or any other form. In this chapter we shall learn the method of finding the length of an arc of a curve. 10.2 Objectives of the chapter By the end of this chapter you should be able to. derive an expression or formula for S, the arc length of a curve if the  Cartesian or parametric equation of the is known. calculate accurately the length of the using the formula.  10.3 Length of an arc S of a curve in Cartesian equation is 1  2 b dx Pr  S dx a ∆y Pn Po P1
v. The cauchy’s principal of the improper integrals b a f ( x ) dx when f(x) has a singularity at c where a ≤ c ≤ b Further reading 1. Advanced Calculus By Watson Fulks John and sons New York. Brisbane Toronto. 94 CHAPTER 10 Length of an Arc of a Curve 10.1 Introduction If you ask a secondary school student to measure the length of an arc of a curve, he will use a string or a flexible material like a string placed upon the arc of the curve and he measures the length of the string placing against a ruler. Also an approximation of length could be found by marking a number of points on the arc and finding the sum of the lengths of all the chords that are small. Any mathematician could do the same method unless he knows the equation of the curve either in Cartesian form or Parametric or any other form. In this chapter we shall learn the method of finding the length of an arc of a curve. 10.2 Objectives of the chapter By the end of this chapter you should be able to.  derive an expression or formula for S, the arc length of a curve if the Cartesian or parametric equation of the is known.  calculate accurately the length of the using the formula. 10.3 Length of an arc S of a curve in Cartesian equation is b S  a 1  dx dx 2 Pr ∆y Pn Po P1
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