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This part of the vol ume counts negatively." }}{PARA 13 "" 1 "" {GLPLOT3D 399 299 299 {PLOTDATA 3 "6(-%%MESHG6#X.%)anythingG6\"6\"^[[[[]\\q^`r\":\":\"$C0000 00000000000C0000000000000003FF0000000000000C000000000000000BFFCAAAAAAA AAAAB3FFCA38E38E38E38C000000000000000BFF95555555555554003F1C71C71C71DC 000000000000000BFF60000000000004008E00000000000C000000000000000BFF2AAA AAAAAAAAB400D1C71C71C71C6C000000000000000BFEEAAAAAAAAAAAC4010538E38E38 E39C000000000000000BFE80000000000014011C00000000000C000000000000000BFE 15555555555574012D38E38E38E39C000000000000000BFD555555555555840138E38E 38E38E3C000000000000000BFC00000000000004013F00000000000C00000000000000 03FB55555555555604013F8E38E38E38EC0000000000000003FD2AAAAAAAAAAAC4013A 8E38E38E38EC0000000000000003FE00000000000004013000000000000C0000000000 000003FE6AAAAAAAAAAAA4011FE38E38E38E4C0000000000000003FED5555555555524 010A38E38E38E3AC0000000000000003FF1FFFFFFFFFFFD400DE00000000004C000000 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y=-2..1-x), x=-2..2); evalf(%);" }{TEXT -1 72 "Notice that the \+ variable limits of integration are handled quite easily." }}{PARA 11 " " 1 "" {XPPMATH 20 "6##\"$C#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"+nmmmu!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "evalf(Int(I nt(f(x,y), y=-2..1-x), x=-2..2)); " }{TEXT -1 94 "If Maple can't do th e integral exactly, you can approximate it numerically using this comm and." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+nmmmu!\")" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 9 "Example 3" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "f:=(x,y) -> 5 + cos(x)*cos(y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF),&\"\"&\" \"\"*&-%$cosG6#9$F/-F26#9%F/F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "p1:=plot3d(\{f(x,y),0\},x=0..3*Pi,y=6*Pi-2*x..6*Pi,ax es=boxed,labels=[\"x axis\",\"y axis\",\"z axis\"]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "p2:=plot3d([x,6*Pi-2*x,z],x=0..3*Pi,z=0.. f(x,6*Pi-2*x)):" }}}{EXCHG 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