MATH 1014 Study Guide - Midterm Guide: Improper Integral

• School: York University
• Department: Mathematics and Statistics
• Course: MATH 1014
• Professor: All

Document Summary

Solutions for class test on february 27, 2012. Math1014 (a) express the length of the curve y between x = 1 and x = 2 as a integral. (1) let y be the curve de ned by y(x) = x2 x. The length of the curve is given by (cid:82) 2 (cid:112)1 + (2x 1)2dx. 2x 1 so the length of the curve is (cid:90) 2. 3 marks (b) do not evaluate the integral from the rst part but explain which of the following facts would be useful in evaluating the integral: (cid:90) sec3( )d = sec( ) tan( ) + ln(sec( ) + tan( )) 2 a + bu a ln|a + bu| + c udu a + bu du a2 + u2 b2. = ln(u + a2 + u2) + c. To evaluate the the integral representing the length of the curve, let tan( ) = Hence the integral becomes (cid:90) arctan(3) (cid:113) arctan(1)