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[]
[null,"Mid-point Integration Rule"]
[null,null,null,null,null,null,null,null,null,null,null,null,"www.numerical-methods.com"]
[null,"This spreadsheet computes the approsimation to an integral using the mid-point integration rule."]
[null,null,null,null,null,null,null,null,null,null,null,null,"source","http://www.numerical-methods.com/integration/Mid-point Integration Rule.xlsm"]
[null,"The integral to be approximated is showm to the right and the function f(x) can be defined using Alt-F11.",null,null,null,null,null,null,null,null,null,null,"guide","http://www.numerical-methods.com/integration/Mid-point Integration Rule.htm"]
[null,"In this example f(x)=EXP(x). The limits a and b on the integral can be set in the yellow cells below."]
[null,"The number of subdomains n can also be set in yellow below."]
[]
[]
[null,null,"a=",0,null,"b=",1]
[]
[null,null," n= (max=100)",5,null,"h=",{"$f":"(b-a)/n","v":0.2}]
[]
[]
[null,"subdomain","mid-pt","f(x^*)"]
[null,"i","x^*"]
[]
[null,1,{"$f":"hh/2","v":0.1},{"$f":"IF(B19<>\"\",f(C19),\"\")","v":1.1051709180756477},null,null,"Integral using Mid-pt rule =",null,null,{"$f":"hh*SUM(D19:D120)","v":1.7154213629958415}]
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[null,{"$f":"IF(B21<n, B21+1,\"\")","v":4},{"$f":"IF(B22<>\"\",C21+hh,\"\")","v":0.7},2.0137527074704766]
[null,{"$f":"IF(B22<n, B22+1,\"\")","v":5},{"$f":"IF(B23<>\"\",C22+hh,\"\")","v":0.89999999999999991},2.4596031111569494]
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