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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 1

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 1

Answers (1)

Answer:

\sin x+\cos x+c

Hint:

Make the function in complete square form and integrate it.

Solution:

Let

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

 

 

 

 

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