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Question: If \(I_{1} = \int_{e}^{e^{2}}{\frac{dx}{\log x}andI_{2} = \int_{1}^{2}{\frac{e^{x}}{x}dx,}}\) then...

If I1=∫ee2dxlog⁡xandI2=∫12exxdx,I_{1} = \int_{e}^{e^{2}}{\frac{dx}{\log x}andI_{2} = \int_{1}^{2}{\frac{e^{x}}{x}dx,}} then

A

I1=I2I_{1} = I_{2}

B

2I1=I22I_{1} = I_{2}

C

I1=2I2I_{1} = 2I_{2}

D

None

Answer

I1=I2I_{1} = I_{2}

Explanation

Solution

= I1=∫ee2dxlog⁡xI_{1} = \int_{e}^{e^{2}}\frac{dx}{\log x} Put log x =t x = ete^{t}

= I1=∫12ettdtI_{1} = \int_{1}^{2}{\frac{e^{t}}{t}dt} = I1=∫12exxdx=I2I_{1} = \int_{1}^{2}{\frac{e^{x}}{x}dx = I_{2}} I1=I2I_{1} = I_{2}