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

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

 

 

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