Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
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
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

This Question is Open

nathanruffBest 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

nathanruffBest 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

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

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

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

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

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

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

mark_o.Best 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.Best 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

nathanruffBest 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.Best 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

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

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

mark_o.Best 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
See more questions >>>
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.