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Mathematics
Calculus
Is there a trick to tell which is the higher curve?
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[QUOTE="zinq, post: 5460394, member: 462505"] Given two curves y = f(x) and y = g(x) on some interval a ≤ x ≤ b, then — unless you know in advance that one curve is greater than the other — they may intersect in some number n of points x[SUB]j[/SUB], say for 1 ≤ j ≤ n, between a and b. To find those points, you would need to solve the equation [INDENT]f(x) = g(x)[/INDENT] for those values of x satisfying the equation and lying between a and b. Then, assuming you are finding the area per se (and not the "signed area"), you would want to [SIZE=4]integrate the absolute value [/SIZE] [INDENT][SIZE=4]|f(x) - g(x)| [/SIZE][/INDENT] [SIZE=4] between each successive pair of x-values x = a, x = x[SUB]1[/SUB], x = x[SUB]2[/SUB], ..., x = x[SUB]n[/SUB], x = b. To do this, you could just test one value in the interior each of the intervals of integration to see whether f(x)-g(x) is positive or negative. (It will not be 0; do you see why?) That will tell you whether [/SIZE] [INDENT][SIZE=4]|f(x) - g(x)| = f(x) - g(x)[/SIZE][/INDENT] [SIZE=4] or [/SIZE] [INDENT][SIZE=4]|f(x) - g(x)| = g(x) - f(x).[/SIZE][/INDENT] [SIZE=4] And finally, add the results together to get the total area between the curves.[/SIZE] [/QUOTE]
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Forums
Mathematics
Calculus
Is there a trick to tell which is the higher curve?
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