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  • Explain solution RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 8 maths

Explain solution RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 8 maths

Answers (1)

Answer:

 (a)

Hint:

 Integration

Given:

 y=log_{e}(x+e),x=log_{e}\left ( \frac{1}{y} \right ),x-axis

Explanation:

\begin{aligned} &x-axis(y=0)\\ &0=log_{e}(x+e)\\ &x+e=e^{0}\\ &x+e=1\\ &x=1-e\\ &x=log_{e}\frac{1}{0}\\ &x=\infty \end{aligned}

Area,

\begin{aligned} &=\int_{1-e}^{0}\left [ log(x+e) \right ]dx+\int_{0}^{\infty }\left [ e^{-x} \right ]dx\\ &=\left [ (x+e)log(x+e) \right ]_{1-e}^{0}-\left [ \frac{(x+e)}{x+e} \right ]_{1-e}^{0}\lim_{k\rightarrow \infty }\left [ -e^{-x} \right ]_{0}^{k}\\ &=e[1-1]-[-1]+\lim_{k\rightarrow \infty }\left [ -e^{-x} \right ]_{0}^{k}\\ &=1+(1-0)\\ &=2 \end{aligned}

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Gurleen Kaur

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