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5.5 part 1

# 5.5 part 1 - 5.5 Change of Variables Cylindrical and...

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Unformatted text preview: 5.5 Change of Variables, Cylindrical and Spherical Coordinates 337 i585 for In Exercises 1 and 2, ﬁnd the region D“ in the (:33) plane corresponding to “ - ' 1: xi '“ - 4-;- .- an. ZUSxSLySI "@szf4?:? :9 ;)a&;év O ..,__. g a f T \$33.23!“; In Exercises 3 and 4, evaluate the given integral by changing to polar coordi- nates. 5- [f (\$2 + y2}3"2da:dy, where D is the disk 32 + 3:2 g 4, D 4. ff fugue-(1y, where D is the semicircle in the ﬁrst two quadrants D bounded by m2 + 3:2 = 9. m 5. Evaluate f e‘mzzdat. -—oo CO 2 6. Evaluate f 38—3” {155. —00 7. Find the normalizing constant c, depending on or, such that N ./ Cerf/O dz = 1. —W 8. Evaluate / tee—”4dr. (Think ﬁrst!) In Exercises 9—12, change the given point from rectangular to cylindrical co- ordinates. 9. (2,1,—2) 10. (0, 3,4) 11.(\ﬂi]11) 12. (—NE, —2. 3) in Exercises 13—16, convert from cylindrical to Cartesian coordinates. 13.(1,w/2,U) 14. (3,45°,82) 15. (1,71r/6,4) ...
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