550 d S x x 3 Find the area under the curve y 1 x from x 1 to x t and evaluate it for t 10 100 and 1000 Then find the total area under this curve for x 1 dx c x x CHAPTER 7 Techniques of Integration 1 11 fx 23 2 dx 21 X 13 S x 1 dx 15 f x x dx x4 1 17 2 dx 19 xe xe do 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 Congngo Leaming All Rights Reserved May not be copied scanned or doplientod in whole or in part Due to clectronic rights somo third party content may be suppressed from the eBook and or oChapter 3 Editorial review has deemed that any suppressed content does not materially affect the overall leaming experienco Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it cos 2t dt 1 So it dx x 12 S 14 S4x dx 16 S 18 31 22 X x 1 x x x3 20 x 1 d dx 100 dx Case 7 S 2x dx 1 9 2x 4 dx 8 dx 10 1 x 4 dx 51 S x y x1 0 y 1 x x M52 S x y x 0 0 y xe 53 S x y 0 x 2 0 y sec x 54 S x y 2 x 0 0 y 1 x 2 55 a If g x sin x x use a calculator or computer to make a table of approximate values of f g x dx for t 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 g x dx is convergent c Illustrate part b by graphing f and g on the same screen for 1x10 Use your graph to explain intuitively why g x dx is convergent