A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
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.)
 2 years ago
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.)

This Question is Open

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

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

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

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

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

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

nathanruff
 2 years ago
Best ResponseYou've already chosen the best response.0\[= \cos \sqrt{x} + C\]Is that correct?

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

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

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

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

nathanruff
 2 years ago
Best ResponseYou've already chosen the best response.0Oh, 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.

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

nathanruff
 2 years ago
Best ResponseYou've already chosen the best response.0Yep! I got my handydandy TI84 Plus. ;)

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.1ok good. did you have the same answer?

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.1ok good. did you have the same answer from your calculator from 2 to 3 ??
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.