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1 format long |
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2 % |
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3 % x^2+y^2 integrated from -1 to 1 in x and -1 to 1 in y = 8/3 |
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4 % |
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5 [bx,by,w]=grule2d(2,2); |
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6 v=gquad2d('gxy',-1,1,-1,1,bx,by,w) |
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7 % or |
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8 v=quad2dg('gxy',-1,1,-1,1) |
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9 % or |
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10 v=gquad2d('gxy',-1,1,-1,1,2,2) |
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11 % or |
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12 n= gquadnd('hx',[-1;-1],[1;1],[2;2]) |
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13 % or |
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14 n=quadndg('hx',[-1;-1],[1;1]) |
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15 correct_ans=8/3 |
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16 % |
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17 % x^2+y^2 integrated from 0 to 2 in x and 0 to 2 in y = 32/3 |
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18 % |
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19 [bx,by,w]=grule2d(2,2); |
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20 vol3=gquad2d('gxy',0,2,0,2,bx,by,w) |
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21 % or |
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22 v=quad2dg('gxy',0,2,0,2) |
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23 % or |
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24 v=gquad2d('gxy',0,2,0,2,2,2) |
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25 % or |
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26 n = gquadnd('hx',[0;0],[2;2],[2;2]) |
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27 % or |
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28 n = quadndg('hx',[0;0],[2;2]) |
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29 correct_ans=32/3 |
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30 % |
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31 % x^2+y^2 integrated from 0 to 3 in x and 0 to 3 in y = 54 |
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32 % |
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33 [bx,by,w]=grule2d(2,2); |
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34 v=gquad2d('gxy',0,3,0,3,bx,by,w) |
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35 % or |
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36 v=gquad2d('gxy',0,3,0,3,2,2) |
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37 % or |
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38 n = gquadnd('hx',[0;0],[3;3],[2;2]) |
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39 correct_ans=54 |
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40 % |
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41 % x^2+y^2 integrated from 0 to 3 in x and 0 to 3 in y = 54 |
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42 % with the general area of intergration (functional limits in x) |
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43 % |
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44 [bx2,wx,by2,wy]=grule2dgen(2,2); |
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45 v=gquad2dgen('gxy','gliml','glimh',0,3,bx2,wx,by2,wy) |
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46 % or |
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47 v=gquad2dgen('gxy','gliml','glimh',0,3,2,2) |
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48 % or |
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49 v=quad2dggen('gxy','gliml','glimh',0,3) |
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50 correct_ans=54 |
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51 % |
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52 % x^2+y^2 integrated from 0 to y in x and 0 to 2 in y = 16/3 |
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53 % |
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54 v=gquad2dgen('gxy','gliml','glimh2',0,2,bx2,wx,by2,wy) |
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55 % or |
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56 v=gquad2dgen('gxy','gliml','glimh2',0,2,2,2) |
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57 correct_ans=16/3 |
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58 % |
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59 % 1 integrated from -sqrt(4-y^2) to sqrt(4-y^2) in x |
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60 % and -2 to 2 in y = 4*pi -- area of circle with radius 2 or (pi r^2) |
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61 % |
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62 v=gquad2dgen('gxy1','lcrcl','lcrcu',-2,2,bx2,wx,by2,wy) |
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63 % or |
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64 v=gquad2dgen('gxy1','lcrcl','lcrcu',-2,2,2,2) |
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65 correct_ans=4*pi |
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66 % --- same problem better quadratue (more points) |
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67 % 1 integrated from -sqrt(4-y^2) to sqrt(4-y^2) in x |
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68 % and -2 to 2 in y = 4*pi -- area of circle with radius 2 or (pi r^2) |
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69 % |
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70 [bx3,wx3,by3,wy3]=grule2dgen(5,5); |
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71 v=gquad2dgen('gxy1','lcrcl','lcrcu',-2,2,bx2,wx,by2,wy) |
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72 % or |
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73 v=gquad2dgen('gxy1','lcrcl','lcrcu',-2,2,5,5) |
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74 correct_ans=4*pi |
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75 % |
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76 % sqrt(x^2+y^2) integrated from -sqrt(4-y^2) to sqrt(4-y^2) in x |
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77 % and -2 to 2 in y = 16*pi/3 |
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78 % |
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79 % Need higher order quadrature |
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80 [bx3,wx3,by3,wy3]=grule2dgen(10,10); |
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81 v=gquad2dgen('gxy2','lcrcl','lcrcu',-2,2,bx3,wx3,by3,wy3) |
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82 % or |
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83 v=gquad2dgen('gxy2','lcrcl','lcrcu',-2,2,10,10) |
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84 correct_ans=16*pi/3 |
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85 % |
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86 % 1/sqrt(1-x^2) integrated from -1 to 1 in x = pi |
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87 % |
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88 % Use Gauss-Chebyshev quadrature |
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89 [bpc,wfc]=crule(2); |
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90 a=gquad('gxy1',-1,1,1,bpc,wfc) |
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91 %or |
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92 a=quadc('gxy1',-1,1) |
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93 correct_ans=pi |
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94 % |
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95 % x^2/sqrt(1-x^2) integrated from -1 to 1 in x = pi/2 |
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96 % |
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97 % Use Gauss-Chebyshev quadrature |
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98 a=gquad('xsquar',-1,1,1,bpc,wfc) |
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99 a=quadc('xsquar',-1,1) |
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100 correct_ans=pi/2 |
