50 3 2 Which of the following integrals are improper Why dx a sec x dx b 5 x d 15 dx 1 S x dx 1 2 3 2 S 3 Find the area under the curve y 1 x from x 1 tox 1 and evaluate it for r 10 100 and 1000 Then find the total area under this curve for x 1 X S 1 dx S x 1 x dx 1 4 29 CHAPTER 7 Techniques of Integration e 17 1 S 1 e 19 fxe dx 21 fcos 21 dr 23 sin a da 25 f x 1x 27 Sze dz In x dx dx dx Copyright 2021 Cengage Learning All Rights Reserved May not be copied scanned or duplicated in whole or in part WCN 02 200 203 Copyright 2021 Cangage Loaming All Rights Reserved May and te orgled scannod or deplicated in whole or in part Due in electric vights sense thint party cratcat may be suppressed from the ellonk and eChapte s Blitorial review has dormed that say upgeessed content does not matorially affect the overall learning experience Cengago Leaming serves the right to remove additional content at any time if absequent rights restrictions require it 12 f 14 16 18 20 22 S 24 1 x 26 o So 30 A x x S 2 1 x x S x 14x 1 x fede dx dx 747 dx 1 dx In x 2 dx 28 ye dy dx sin 0 e do dv S 4 20 3 dx dx 5 48 Determine whether the integral is convergent or divergent Evaluate integrals that are convergent 6 5 2x dx 7 Se dx 9 2x 4 dx 8 10 dx 51 S x y x1 0 y 1 x x YM 52 S x y x 0 0 y xe 53 S x y 0 x 2 0 y scc x M 54 S x y 2 x 0 0 y 1 x 2 dx x 4 MM 56 a If g x 1 x dx M55 a If g x sin x x use a calculator or computer to make a table of approximate values of f g x dx fort 2 5 10 100 1000 and 10 000 Does it appear that f g x dx is convergent b Use the Comparison Theorem with f x 1 x to show that f g x dx is convergent c Illustrate part b by graphing and g on the same screen for 1x10 Use your graph to explain intuitively why g x dx is convergent 1 use a calculator or computer to make a table of approximate values of g x dx for 5 10 100 1000 and 10 000 Docs it appear that g x dx is convergent or divergent b Use the Comparison Theorem with f x 1 x to show that f g x dx is divergent c Illustrate part b by graphing fand g on the same screen for 2 x 20 Use your graph to explain intuitively why g x dx is divergent 57 64 Use the Comparison Theorem to determine whether the