Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Questions  >>  CBSE XII  >>  Math  >>  Integrals
Answer
Comment
Share
Q)

Choose the correct answer in $\Large \int \normalsize\frac{dx}{\sin^2x\cos^2x}$ equals

$\begin{array}{1 1} (A)\;\tan x+\cot x+C & (B)\;\tan x-\cot x+C\\(C)\;\tan x\cot x+C & (D)\;\tan x-\cot2x+C\end{array}$

1 Answer

Comment
A)
Toolbox:
  • (i)Method of substitution :
  • Given f(x)dx can be transformed into another form by changing independent variable x to t by substituting x=g(t).
  • Consider $I=\int f(x)dx.$
  • Put x=g(t) so that $\frac{dx}{dt}=g'(t).$
  • $\Rightarrow $dx=g'(t)dt.
  • Thus $I=\int f(g(t).g'(t))dt.$
Given $I=\int \frac{dx}{\sin^2x\cos^2x}dx$.
 
We know $\sin^2x+\cos^2x=1.$
 
Hence we can write I as,
 
$I=\int \frac{\sin^2x+\cos^2x}{\sin^2x\cos^2x}dx.$
 
Now separating the terms we get,
 
$I=\int \big(\frac{1}{\cos^2x}+\frac{1}{\sin^2x}\big)dx$.
 
But $\frac{1}{\cos^2x}=\sec^2x$ and $\frac{1}{\sin^2x}=cosec^2x.$
 
$\;\;=\int\sec^2xdx+\int cosec^2xdx.$
On integrating we get,
 
$\tan x-cot x+c.$
 
Hence the correct answer is B.

 

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.
...