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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 35 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 35 Maths Textbook Solution.

Answers (1)

Answer: 3\sin ^{-1}x,x+3\sqrt{1-x^{2}}+c

Given: \int \sin ^{-1}\left ( 3x-4x^{3} \right )dx

Hint:

        3x-4x^{3}\rightarrow \sin \theta

         x=\sin \: t

Solution:

            I=\int \sin ^{-1}\left ( 3x-4x^{3} \right )dx

                                Let x = sint  =>dx = costdt & 3\: \sin t-4\sin ^{3}t=\sin 3t

           \begin{aligned} &=\int \sin ^{-1} \sin 3 t \cos t d t \\ &=\int 3 t \cos t d t \\ &=3 \int t \cos t d t \\ &I=3\left[\left(t \int \cos t d t-\int(1 \sin t) d t\right)\right] \\ &=3\left[t \sin t-\int \sin t d t\right] \\ &=3[t \sin t-(-\cos t+c)] \\ &=3 t \sin t+3 \cos t+c \\ &=3 \sin ^{-1} x \cdot x+3 \sqrt{1-x^{2}}+c \end{aligned}

 

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