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  • Please solve RD Sharma class 12 chapter 20 Areas of Bounded Region exercise multiple choice question 1 maths textbook solution

Please solve RD Sharma class 12 chapter 20 Areas of Bounded Region exercise multiple choice question 1 maths textbook solution

Answers (1)

Answer:

 1(b)

Hint:

 Make the graph of 2kx and then apply integration

Given:

 y=2^{kx} \text { and } x=0, \quad x=2 \text { is }\frac{3}{log_{e}2}

Explanation:

Area of the bounded region

=\int_{0}^{2}2^{kx}dx

\begin{aligned} &\frac{3}{log_{e}2}=\int_{0}^{2}2^{kx}dx \\ &\frac{3}{log_{e}2}=\left [ \frac{2^{kx}}{log_{e}2} \right ]_{0}^{2} \\ &3=\left [ 2^{kx} \right ]_{0}^{2} \\ &3=(2^{k})^{2}-(2^{k})^{0} \\ &3=2^{2k}-1 \end{aligned}                                \begin{aligned} &\left [ \because \int a^{x}dx=\frac{a^{x}}{log_{e}a} \right ] \\ &\left [ \because a^{0}=1 \right ] \end{aligned}

\begin{aligned} &4=2^{2k} \\ &2^{2}=2^{2k} \\ &2k=2 \\ &k=1 \end{aligned}

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Gurleen Kaur

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