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  • Please solve RD Sharma class 12 chapter 19 Definite Integrals exercise Multiple choice question 26 maths textbook solution

Please solve RD Sharma class 12 chapter 19 Definite Integrals exercise Multiple choice question 26 maths textbook solution

Answers (1)

best_answer

Answer:

(\log x)^{-1}(x-1) x

Given:

\int_{x^{2}}^{x^{3}} \frac{1}{\log _{e} t} d x

Hint:

This equation will solve byf'(x)formula.
 

Solution:

\begin{aligned} &f^{\prime}(x)=\frac{1}{\log x^{3}} \cdot 3 x^{2}-\frac{1}{\log x^{2}} \cdot(2 x) \\\\ &f^{\prime}(x)=\frac{3 x^{2}}{3 \log x^{3}}-\frac{2 x}{2 \log x^{2}} \end{aligned}

\begin{aligned} f^{\prime}(x) &=\frac{x^{2}}{\log x}-\frac{x}{\log x} \\\\ &=\frac{x^{2}-x}{\log x} \end{aligned}

           \begin{aligned} &=\frac{x(x-1)}{\log x} \\\\ &=(\log x)^{-1}(x-1) x \end{aligned}

 

 

 

Posted by

infoexpert26

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