Get Answers to all your Questions

header-bg qa

Provide Solution For R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Revision Exercise Question 70 Maths Textbook Solution.

Answers (1)

Answer:

\tan x+\frac{(\tan x)^{3}}{3}+c

Hint:

To solve the given statement split the sec? x into sec² x sec²x then apply the formula.

Given:

\int \sec ^{4} x d x

Solution:

I=\int \sec ^{4} x d x

   1+\tan ^{2} x=\sec ^{2} x

=\int\left(1+\tan ^{2} x\right) \sec ^{2} x d x

=\int\left(1+t^{2}\right) d t                                            \left[\because \tan x=t, \sec ^{2} x d x=d t, \int x^{n} d x=\frac{x^{n}+1}{n+1}+c\right]

=t+\frac{t^{3}}{3}+c

=\tan x+\frac{(\tan x)^{3}}{3}+c

 

 

Posted by

infoexpert21

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads