A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
i need some help here my friends :)
\[\left \int_{1}^{\sqrt{3}} \frac{e^{x} \sin x}{1+x^2} dx \right \le \frac{\pi}{2 e}\]
 2 years ago
i need some help here my friends :) \[\left \int_{1}^{\sqrt{3}} \frac{e^{x} \sin x}{1+x^2} dx \right \le \frac{\pi}{2 e}\]

This Question is Closed

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0yikes did you try the simple method of locating the max on the interval? i am just asking, i didn't go it, or not sure this will work

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0i think that will not work if im not wrong...

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0@satellite73 i tried it but no good results.

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1first we use theorem if a<b\[\left \int\limits _a^b f(x)dx \right\le \int\limits_a^b \left f(x) dx\right\] \[\left \int\limits_1^\sqrt{3} \frac{e^{x}\sin x}{1+x^2}dx \right\le \int\limits_1^\sqrt{3} \left\frac{e^{x}\sin x}{1+x^2}dx \right\] \[\le \int\limits_1^\sqrt{3}\frac{1}{e(1+x^2)}=\frac{1}{e}\tan^{1}x _1^\sqrt{3}=\frac{1}{e}(\tan^{1}\sqrt{3}\tan^{1}1)=\frac{1}{e}(\pi/3\pi/4)=\frac{\pi}{12e}\] \[\square\]
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.