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  • Provide solution for RD sharma maths class 12 chapter 20 Areas Of Bounded Region exercise Fill in the blanks question 5

Provide solution for RD sharma maths class 12 chapter 20 Areas Of Bounded Region exercise Fill in the blanks question 5

Answers (1)

best_answer

2 \log 2

Hint:

Use indefinite integral formula then put limits to solve this integral

Given:

y=\tan x, x-axis\\ x=\frac{-\pi}{3}, x=\frac{\pi}{3}

Explanation:

\begin{aligned} &\int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} \tan x d x=2 \int_{0}^{\frac{\pi}{3}} \tan x d x\\ &=[-2 \log \cos x]_{0}^{\frac{\pi}{3}}\\ \end{aligned}

\begin{aligned} &\begin{aligned} &=-2\left[\log \cos \frac{\pi}{3}-\log \cos 0\right] \\ &=-2\left[\log \frac{1}{2}-0\right] \\ &=-2 \log \frac{1}{2} \\ &=-2[\log 1-\log 2] \end{aligned} \quad\left[\begin{array}{l} \because \int_{-a}^{a} f(x) d x=2 \int_{0}^{a} f(x) d x \\ \because \int \tan x d x=-\log \cos x+c \\ \because[\log m-\log n]=\log \frac{m}{n} \\ \because \log 1=0 \end{array}\right]\\ &=2 \log 2 s q \cdot \text { units } \end{aligned}

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