s(m) gives the location to evaluate the function in the mth partition
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式13: "s" left parenthesis, "m" , right parenthesis equals "a" plus "w" left parenthesis, "m" plus "c" , right parenthesissm=a+wm+c
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m_x(x) is the number of the partition for x
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式15: "m" Subscript, "x" , Baseline left parenthesis, "x" , right parenthesis equals floor left parenthesis, StartFraction, left parenthesis, "x" minus "a" , right parenthesis Over "w" , EndFraction , right parenthesismxx=floorx−aw
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式16: "s" Subscript, "x" , Baseline left parenthesis, "x" , right parenthesis equals left brace, "a" less than or equal to "x" less than or equal to "b" : "s" left parenthesis, "m" Subscript, "x" , Baseline left parenthesis, "x" , right parenthesis , right parenthesis , right bracesxx=a≤x≤b:smxx
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式17: "g" left parenthesis, "s" Subscript, "x" , Baseline left parenthesis, "x" , right parenthesis , right parenthesis less than or equal to "y" less than or equal to "f" left parenthesis, "s" Subscript, "x" , Baseline left parenthesis, "x" , right parenthesis , right parenthesisgsxx≤y≤fsxx
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式18: "f" left parenthesis, "s" Subscript, "x" , Baseline left parenthesis, "x" , right parenthesis , right parenthesis less than or equal to "y" less than or equal to "g" left parenthesis, "s" Subscript, "x" , Baseline left parenthesis, "x" , right parenthesis , right parenthesisfsxx≤y≤gsxx
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Estimate for Area
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式20: "A" equals "w" times Start sum from "n" equals 0 to "n" minus 1, end sum, absolute value left parenthesis, "f" left parenthesis, "s" left parenthesis, "n" , right parenthesis , right parenthesis minus "g" left parenthesis, "s" left parenthesis, "n" , right parenthesis , right parenthesis , right parenthesisA=w·n−1∑n=0absfsn−gsn
