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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 2

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 2

Answers (1)

Answer:

-\sin x-\cos x+c

Hint:

Simplify it and integrate it.

Solution:
\begin{aligned} &I=\int \sqrt{1-\sin 2 x} d x \\ &I=\int \sqrt{\cos ^{2} x+\sin ^{2} x-2 \sin x \cos x} d x \quad\quad\quad\quad\quad\quad\quad\left[\cos ^{2} x+\sin ^{2} x=1, \sin 2 x=2 \sin x \cos x\right] \\ &\Rightarrow I=\int \sqrt{(\sin x-\cos x)^{2}} d x \end{aligned}
\begin{aligned} &I=\int(\sin x-\cos x) d x \\ &I=\int \sin x d x-\int \cos x d x \\ &I=-\cos x-\sin x+c \end{aligned}

 

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