ESE 318-02, Spring 2016 Homework Set #12 Due Tuesday, Apr. 19 1. Zill 9.10.15. 2. Zill 9.10.16. Can use integration by parts, or a Table. 3. Zill 9.10.21. 4. Zill 9.10.39. Can use integral table in Zill text. 5. Zill 9.10.40. 6. Zill 9.11.8. 7. Zill 9.11.25. 8. Zill 9.11.28. 9. Zill 9.11.29. OK to use Table of integrals. 10. Zill 9.11.31. Solutions 1. Zill 9.10.15 Area is between y = x2 and y = x3, for 0 < x < 1.         842574324282172314110772331441106231036424310210322222222142142,1422323 xxxdxxxxdxxxxxxxdxyyxydxdyyxdAyxxyxydAyxxxyxxRRESE 318-02, Spring 2016 2. Zill 9.10.16. Can use integration by parts, or a Table.      2121101010211010101010010 0111)(1,0,dAxeeeTableorpartsbydxedvxudxexedxxedxxexdxdxxedxxxedxxedxdyxedAxexyxydAxeRyxxxxxxxxyyxyRyRy 3. Zill 9.10.21. Area is the triangle from y = -x to y = x, for 0 < x < sqrt(3).       31432322/332302/3232302302302221841121113,,1 xdxxxdxxydxdyxdAxxyxyxdAxxxyxxRRESE 318-02, Spring 2016 4. Zill 9.10.39. Draw a picture of the region of integration.          842112111211021212102221104100410 0410141tan0tan1tantan2211111111yydyduyuydyydyyydyyxdydxydxdyyyxxyx 5. Zill 9.10.40 Draw a picture of the region of integration.      9522/392202/3332312032312032200320 03402319113111122  xdxxxdxxxdxxydxdyxdydxxxyxyESE 318-02, Spring 2016 6. Zill 9.11.8. The region of integration is just the circle of radius 5.   32502031252050331205022050222220500,25,ddrddrrdrdrrrrzzyxyxz 7. Zill 9.11.25 See that the region of integration is a half disc.  9030sincos3033130200303390222 rdrrddrrdrdxdyyxrryrxx 8. Zill 9.11.28.   dxdyyxx2022sin The region of integration is the upper half-disc of radius . (Should graph it.)           20coscoscos2sinsinsin01022022100sin22100 0202222222rrdrrddrdrrdxdyyxrryxduuxESE 318-02, Spring 2016 9. Zill 9.11.29. See that the region of integration is the annulus shown. Can use table for cos2. 834232140222104122242/02/02223212122121212/022/02122/0212222140222104122222222222212sin4121cos2sin4121cos:2coscoscos020sincos      dxdyyxxdxdyyxxdCuuuduTablerrdrrdrdddrrdrdrrrdxdyyxxdxdyyxxrryrxxxxxxx 10. Zill 9.11.31 The region of integration is the top semi-circle of radius 5.           250113cos3sin4sin3cos4sin3cos4sin3cos434050sincos312500503310502050205020502050552502