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

Answers (1)

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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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