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  • please solve RD sharma class 12 chapter 20 Areas Of Bounded Region exercise Fill in the blanks question 3 maths textbook solution

please solve RD sharma class 12 chapter 20 Areas Of Bounded Region exercise Fill in the blanks question 3 maths textbook solution

Answers (1)

2c \log_{e}2 sq. units

Hint:

Use indefinite integral formula then put limits to solve this integral

Given:

xy=c,x-axis\\x=1,x=4

Explanation

Required area,

\begin{aligned} &=\int_{1}^{4} \frac{c}{x} d x\\ \end{aligned}

\begin{aligned} &\begin{aligned} &=c\left[\log _{e} x\right]_{1}^{4} \\ &=c\left[\log _{e} 4-\log _{e} 1\right] \\ &=c \log _{e} 4 \end{aligned} \quad\left[\begin{array}{l} \because \int_{a}^{b} \frac{1}{x} d x=[\log x]_{a}^{b} \\ \because \log _{e} 1=0 \end{array}\right]\\ \end{aligned}

\begin{aligned} &=c \log _{e} 2^{2}\\ &=2 c \log _{e} 2 \mathrm{sq} \cdot \text { units } \end{aligned}

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