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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)

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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