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  • Provide solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Multiple choice question 14

Provide solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Multiple choice question 14

Answers (1)

best_answer

Answer:

1

Given:

\int_{1}^{\theta} \frac{\log x}{x} d x

Hint:

Using by parts.

Explanation:  

Let

\begin{aligned} I &=\int_{1}^{e} \log x d x \\\\ &=\left[\log x \int 1 d x-\int \frac{d}{d x}(\log x)-\int d x\right]_{1}^{e} \end{aligned}

\begin{aligned} &=\left[x \log x-\int \frac{1}{x} \cdot x d x\right]_{1}^{e} \\\\ &=[x \log x-x]_{1}^{e} \end{aligned}

 

\begin{aligned} &=[x(\log x-1)]_{1}^{e} \\\\ & \\\\ &=1[0-1]=1 \end{aligned}

 

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infoexpert26

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