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  • Provide solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Very short answer type question 22

Provide solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Very short answer type question 22

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Answer: \frac{1}{2} \log 2

Hint: you must know the rule of integration for function of x

Given: \int_{0}^{\frac{\pi}{4}} \tan x\; d x

Solution:  \int_{0}^{\frac{\pi}{4}} \tan x\; d x

\begin{aligned} &=\log [\sec x]_{0}^{\frac{\pi}{4}} \\\\ &=\log \left(\sec \frac{\pi}{4}\right)-\log (\sec 0) \\\\ &=\log |\sqrt{2}|-\log |1| \end{aligned}

\begin{aligned} &=\log \sqrt{2}-0 \\\\ &=\log \sqrt{2} \\\\ &=\log (2)^{\frac{1}{2}} \\\\ &=\frac{1}{2} \log 2 \end{aligned}

 

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