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  • Explain solution RD Sharma class 12 Chapter 19 Definite Integrals Exercise 19.3 question 11

Explain solution RD Sharma class 12 Chapter 19 Definite Integrals Exercise 19.3 question 11

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Answer:  0

Hint: You must know the rules of solving definite integral.

Given:   \int_{0}^{\frac{\pi}{2}}|\cos 2 x| d x

Solution:

                \int_{0}^{\frac{\pi}{2}}|\cos 2 x| d x

We know that  |\cos 2 x|=\left\{\begin{array}{ll} -\cos 2 x & \frac{\pi}{4} \leq x \leq \frac{\pi}{2} \\\\ \cos 2 x & 0<x \leq \frac{\pi}{4} \end{array}\right\}

\begin{aligned} &\therefore I=\int_{0}^{\frac{\pi}{2}}|\cos 2 x| d x \\ & \end{aligned}

\Rightarrow I=\int_{0}^{\frac{\pi}{4}} \cos 2 x d x-\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \cos 2 x d x

\begin{aligned} &\Rightarrow I=\left[\frac{\sin 2 x}{2}\right]_{0}^{\frac{\pi}{4}}-\left[\frac{\sin 2 x}{2}\right]_{\frac{\pi}{4}}^{\frac{\pi}{2}} \\ & \end{aligned}

\Rightarrow I=\frac{1}{2}-0-0+\frac{1}{2} \\

\Rightarrow I=1

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