Higher math proficiency test: An extended-problem-solving skill evaluation tool

Re:Higher math proficiency test: An extended-problem-solving... by SamReidHughes on Friday July 24, 2020 @02:15PM (#23942746)

The function is non-negative on [-pi/4, pi/4], so you don't need any assumption about area meaning "signed area."

Your math is wrong on that problem. The integral of sin^2 over [-pi/4, pi/4] is (pi - 2)/4, which was one of the options. The functions sin^2 and cos^2 only have equal integrals over properly aligned quarter-cycles like [0, pi/2].

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Re:Higher math proficiency test: An extended-problem-solving... by virtuous_signal on Friday July 24, 2020 @02:23PM (#23942850)

The second summand due to the sin^3 is not nonnegative (so you do need to use oddness to avoid the integral)

Right on the second part, my bad.

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Re:Higher math proficiency test: An extended-problem-solving... by SamReidHughes on Friday July 24, 2020 @02:25PM (#23942877)

I read that part of your comment as re-interpreting the question, instead of just reinterpreting the prior part of the sentence it's in, never mind.

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Re:Higher math proficiency test: An extended-problem-solving... by virtuous_signal on Friday July 24, 2020 @02:32PM (#23942962)

Regardless -- I think it's a valid reading to say the "area between" say, g(x) = x and the x-axis from -1 to 1 equals 1. Only people who are trained would say it's 0. So I don't think something like that really measures "extended problem solving and deductive thinking skills" which is a pretty lofty goal for a test.

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