Proof that Ratio of A : B = 1 | Desmos

Expression 4: "f" left parenthesis, "x" , right parenthesis equals StartFraction, "x" squared Over 1 plus "x" squared , EndFraction StartRoot, StartFraction, 1 minus "x" Over 1 plus "x" , EndFraction , EndRoot Has graph. To audio trace, press ALT+T.

4

Expression 5: "A" equals Start integral from 0 to 1, end integral, StartFraction, "x" squared Over 1 plus "x" squared , EndFraction StartRoot, StartFraction, 1 minus "x" Over 1 plus "x" , EndFraction , EndRoot "d" "x" equals 0.0 8 3 3 0 0 8 3 2 3 9 5 5

equals

0.0 8 3 3 0 0 8 3 2 3 9 5 5

5

Expression 6: "B" equals StartFraction, ln left parenthesis, 1 plus StartRoot, 2 , EndRoot , right parenthesis Over StartRoot, 2 , EndRoot , EndFraction plus left parenthesis, 1 minus StartFraction, 1 Over StartRoot, 2 , EndRoot , EndFraction , right parenthesis StartFraction, pi Over 2 , EndFraction minus 1 equals 0.0 8 3 3 0 0 8 3 2 3 9 5 5

equals

0.0 8 3 3 0 0 8 3 2 3 9 5 5

6

Expression 7: "c" Subscript, 1 , Baseline equals hsv left parenthesis, 60 , 1 , 1 , right parenthesis equals light yellow

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