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nathanruff
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Use the fact that the function is odd to show that the inequality is true. (Anyone who helps me will receive a medal because I'm stuck.)
 one year ago
 one year ago
nathanruff Group Title
Use the fact that the function is odd to show that the inequality is true. (Anyone who helps me will receive a medal because I'm stuck.)
 one year ago
 one year ago

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nathanruff Group TitleBest ResponseYou've already chosen the best response.0
I already verified that the function is odd. I just need help showing that: \[0 \le \int\limits_{2}^{3}\sin \sqrt[3]{x}dx \le 1\]
 one year ago

nathanruff Group TitleBest ResponseYou've already chosen the best response.0
Using the fact that the function is odd I know that\[0 \le \int\limits_{2}^{3}\sin \sqrt[3]{x}dx \le 1 = 0 \le \int\limits_{2}^{3}\sin \sqrt[3]{x}dx \le 1\]
 one year ago

nathanruff Group TitleBest ResponseYou've already chosen the best response.0
Now, I just need to show that \[0 \le \int\limits_{2}^{3}\sin \sqrt[3]{x}dx \le 1\]
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
is it like this \[\sin ^{2}(\sqrt{x}) ?\]
 one year ago

nathanruff Group TitleBest ResponseYou've already chosen the best response.0
It's actually\[\sin (\sqrt[3]{x})\] or \[\sin(x^{1/3})\]
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
what did you get on this one? \[\int\limits_{}^{}\sin \sqrt{x}dx= ?\]
 one year ago

nathanruff Group TitleBest ResponseYou've already chosen the best response.0
\[= \cos \sqrt{x} + C\]Is that correct?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
no, you need to consider (x)^1/2=u,.....
 one year ago

nathanruff Group TitleBest ResponseYou've already chosen the best response.0
Ah, u substitution.
 one year ago

nathanruff Group TitleBest ResponseYou've already chosen the best response.0
\[= \cos \sqrt{x}+C\] Wouldn't that be it?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
if we let u=x^1/2 du=1/(2x^1/2)dx
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
youll come up to = 2 sin x^1/2 2 x^1/2 cos x^1/2 ] from 2 to 3
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
is it from 2 to 3?
 one year ago

nathanruff Group TitleBest ResponseYou've already chosen the best response.0
Oh, okay. To begin with, it's from 2 to 3, but the integral from 2 to 0 and the integral from 0 to 2 cancel each other out this the function is odd and symmetric about the origin, so in its simplest form, the integral is from 2 to 3.
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
do you have a calculator that does derivative and integrals? that way you can re check your work... :D
 one year ago

nathanruff Group TitleBest ResponseYou've already chosen the best response.0
Yep! I got my handydandy TI84 Plus. ;)
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
ok good. did you have the same answer?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
ok good. did you have the same answer from your calculator from 2 to 3 ??
 one year ago

nathanruff Group TitleBest ResponseYou've already chosen the best response.0
Yep. Thank you!
 one year ago
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