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}} min ^m \{ \tan x , \cot x \} dx$

\[\begin {array} {1 1} (a)\;\log \sqrt 2 \\ (b)\;\log 2 \sqrt 2 \\ (c)\;\log(\frac{1}{2}) \\ (d)\;\log 2 \end {array}\]

1 Answer

Comment
A)
To solve this type are throw graph. to $min ^m$, take lower portion.
=> $\int \limits_0^{\large\frac{\pi}{4}}$$ \tan x dx + \int \limits ^{\large\frac{\pi}{2}}_{\frac{\pi}{4}} \cot x dx$
=>$ \bigg[\log |\sec x|\bigg]_0^{\large\frac{\pi}{4}}+ \bigg[ \log |\sin x| \bigg]_{\frac{\pi}{4}}^{\frac{\pi}{2}}$
=> $\log | \sec \large\frac{\pi}{4}|$$ - | \sec 0| + \log | \sin \large\frac{z}{2}|$$ - \log \sin \large\frac{\pi}{2}$
=> $ \log \sqrt 2 -\log (1) + \log |1| - \log | \large\frac{1}{\sqrt 2}|$
=> $2 \log \sqrt 2$
=> $\log (\sqrt (2)^2)$
=> $ \log_e^2$
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.
...