Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
Answer
Comment
Share
Q)

Integrate : $\int \limits_0^{\large\frac{\pi}{2}} \large\frac{\cos ^3 x}{\sin ^3 x + \cos ^3 x }$$ dx$

$ (A)\;\large\frac{\pi}{2} \\ (B)\;\large\frac{\pi}{4} \\ (C)\;2 \pi \\ (D)\;\large\frac{\pi}{6} $

1 Answer

Comment
A)
$f(x) = \int \limits_0^{\large\frac{\pi}{2}} \large\frac{\cos ^3 x}{\sin ^3 x + \cos ^3 x }$$ dx$... (1)
By using properties $f(x)= f( \large\frac{\pi}{2}$$-x)$
$f(\large\frac{\pi}{2}$$ - x)=>$ $\int \limits_0^{\large\frac{\pi}{2}} \large\frac{\cos ^3 (\Large\frac{\pi}{2}-x)}{\sin^3 (\large\frac{\pi}{2}-x) + \cos ^3 (\Large\frac{\pi}{2}-x)}$$dx$
$f(\large\frac{\pi}{2}$$-0)=>$ $\int \limits_0^{\large\frac{\pi}{2}} \large\frac{\sin ^3 x}{\cos ^3 x +\sin ^3 x}$----(2)
adding (1) and (2) we get,
$f(x) +f(\large\frac{\pi }{2} $$-x)=\int \limits_0^{\large\frac{\pi}{2}}$$ dx$
$2f(x)=\large\frac{z}{2}$$ [1-0]$
$f(x)= \large\frac{\pi}{4}$
Hence b is the correct answer.
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...