Get Answers to all your Questions

header-bg qa

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.18 Question 10 Maths Textbook Solution.

Answers (1)

Answer: \log \left|\sin ^{2} x+2+\sqrt{\sin ^{4} x+4 \sin ^{2} x-2}\right|+c

Hint Let \sin ^{2} x=t

Given: \int \frac{\sin 2 x}{\sqrt{\sin ^{4} x+4 \sin ^{2} x-2}} d x


              \int \frac{\sin 2 x}{\sqrt{\sin ^{4} x+4 \sin ^{2} x-2}} d x.................(1)

            Let  \sin ^{2} x=t

            2 \sin x \cos x d x=d t

            \sin 2 x d x=d t                                                  (Differentiate w.r.t to t)

From (1) we have

                \int \frac{d t}{\sqrt{t^{2}+4 t-2}}

              =\int \frac{d t}{\sqrt{t^{2}+4 t+4-4-2}}

              =\int \frac{d t}{\sqrt{(t+2)^{2}-6}}

              Let t+2 = u                                                                        (Differentiate w.r.t to u)


               =\int \frac{d u}{\sqrt{u^{2}-6}}

               =\log \left|u+\sqrt{u^{2}-6}\right|+c

               =\log \left|t+2+\sqrt{(t+2)^{2}-6}\right|+c

               =\log \left|\sin ^{2} x+2+\sqrt{\sin ^{4} x+4 \sin ^{2} x-2}\right|+c\left[\because \int \frac{d x}{\sqrt{x^{2}-a^{2}}}=\log \left|x+\sqrt{x^{2}-a^{2}}\right|+c\right]

Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support