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anonymous
 5 years ago
From my calc book:
"Since the integrand is an odd function, integral_(2)^(2) (x^3)*(16x^2)^1/2 dx = 0"
My question: Why?!
anonymous
 5 years ago
From my calc book: "Since the integrand is an odd function, integral_(2)^(2) (x^3)*(16x^2)^1/2 dx = 0" My question: Why?!

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{2}^{2}x^3\sqrt{16x^2}dx = 0\] <A little easier to view

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Also, I understand the trig substitution for the indefinite integral but I don't know why this definite integral is 0 and what an odd function is referring to.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0odd function is because the highest degree of x is 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and it is equal to 0 since the are from 2 to 0 "cancels" out the area from 0 to 2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Will this usually happen for odd functions where it will "cancel" out?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no unless it's an improper integral
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