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  • Please Solve R .D. Sharma class 12 Chapter 19 Definite Integrals Exercise 19.1 Question 11 Maths textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 19 Definite Integrals Exercise 19.1 Question 11 Maths textbook Solution.

Answers (1)

Answer: \frac{1}{2}log2

Hint: Use indefinite formula to solve the integral and then put the value of limit to get the required answer

Given: \int_{\frac{\pi }{4}}^{\frac{\pi }{2}}\cot xdx

Solution:\int_{\frac{\pi }{4}}^{\frac{\pi }{2}}\cot xdx=\left [ log|\sin x| \right ]^{\frac{\pi }{2}}_{\frac{\pi }{4}}                                        \left ( \int \cot xdx=log|\sin x| \right )

=\left [ log|\sin \frac{\pi }{2} |-|\sin \frac{\pi }{4}|\right ]

=log1-log\frac{1}{\sqrt{2}}                                                                                            \left [ \sin \frac{\pi }{2} =1,\sin \frac{\pi }{4}=\frac{1}{\sqrt{2}}\right ]

\begin{aligned} &=\log \frac{1}{\frac{1}{\sqrt{2}}} \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \quad\left[\log a-\log b=\log \frac{a}{b}\right] \\ &=\log \sqrt{2}=\log 2^{\frac{1}{2}} \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;\quad\left[\log a^{m}=m \log a\right] \end{aligned}

=\frac{1}{2}log2

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