Expresión 4: "f" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals left brace, 0 less than or equal to "x" less than or equal to cos left parenthesis, StartFraction, varphi Over 2 , EndFraction , right parenthesis : tan left parenthesis, StartFraction, varphi Over 2 , EndFraction , right parenthesis "x" , "x" greater than cos left parenthesis, StartFraction, varphi Over 2 , EndFraction , right parenthesis : StartRoot, sin squared left parenthesis, StartFraction, varphi Over 2 , EndFraction , right parenthesis minus left parenthesis, "x" minus cos left parenthesis, StartFraction, varphi Over 2 , EndFraction , right parenthesis , right parenthesis squared , EndRoot , right bracef1x=0≤x≤cosφ2:tanφ2x,x>cosφ2:sin2φ2−x−cosφ22
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Expresión 5: "f" Subscript, 2 , Baseline left parenthesis, "x" , right parenthesis equals negative "f" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesisf2x=−f1x
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Expresión 6: min left parenthesis, 0 , "f" Subscript, 2 , Baseline left parenthesis, "x" , right parenthesis , right parenthesis less than or equal to "y" less than or equal to max left parenthesis, 0 , "f" Subscript, 2 , Baseline left parenthesis, "x" , right parenthesis , right parenthesis left brace, 0 less than or equal to "x" less than or equal to beta , right bracemin0,f2x≤y≤max0,f2x0≤x≤β
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Expresión 7: min left parenthesis, 0 , "f" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis , right parenthesis less than or equal to "y" less than or equal to max left parenthesis, 0 , "f" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis , right parenthesis left brace, 0 less than or equal to "x" less than or equal to beta , right bracemin0,f1x≤y≤max0,f1x0≤x≤β
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Expresión 8: "A" equals 2 Start integral from 0 to beta , end integral, "f" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis "d" "x"A=2∫β0f1xdx
