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  • Need solution for RD Sharma Maths Class 12 Chapter 19 Definite Integrals Excercise 19.3 Question 23

Need solution for RD Sharma Maths Class 12 Chapter 19 Definite Integrals Excercise 19.3 Question 23

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Answer:  0

Hint: We will use the property of definite integrals.

Given:  \int_{0}^{\pi} \cos x|\cos x| d x

Solution:

                I=\int_{0}^{\pi} \cos x|\cos x| d x                                                       … (i)

Consider,  f(x)=\cos x|\cos x|

Now, use the property:   \int_{0}^{a} f(x) d x=\int_{0}^{a} f(a-x) d x

                 I=\int_{0}^{\pi} \cos (\pi-x)|\cos (\pi-x)| d x \\

                =\int_{0}^{\pi}-\cos (x)|\cos (x)| d x \\

                \begin{aligned} & &I=\int_{0}^{\pi}-\cos (x)|\cos (x)| d x \end{aligned}                                       … (ii)

Adding (i) and (ii) , we get

                \begin{aligned} &2 I=0 \\ & \end{aligned}

                I=0

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