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  • Need solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Fill in the blanks question 7

Need solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Fill in the blanks question 7

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Answer: \frac{e^{2}}{2}-e

Hint: Using \int e^{x}\left(f(x)+f^{\prime}(x)\right) d x  and integration by parts. 

Given:\int_{1}^{2} e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right)dx

Solution:  

\mathrm{I}=\int_{1}^{2} e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right) \mathrm{dx}

    =\int_{1}^{2} e^{x}\left(\frac{1}{x}\right) d x-\int_{1}^{2} e^{x}\left(\frac{1}{x^{2}}\right) d x

    

    

    \begin{aligned} &=\left[\frac{e^{2}}{2}\right]-\left[\frac{e^{1}}{1}\right] \\\\ &=\frac{e^{2}}{2}-e \end{aligned}

 

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