2

∫ | log₁₀​x | dx equals to

½

1. log₁₀(8/e)
2. ½ log₁₀(8/e)
3. log₁₀(2/e)
4. None of these

Ans is option b

Explanation-

First check on which point is the fumction log x is 0

It will come as 1 . Hence at 1 the function is discontinuous and the imtegral will break im twoo parts-

1) solve the function with limit from 1/2 to 1 . Also whithin this range mod is negative so multiply -1 amd open the mod and solve.

2) solve the function with limit from 1 to 2 . The function is positive in this range so remove the mod and write the function as it is and solve the integral.

Now combine the answeres of 1 an 2 an rearrange using log properties. The answer will come as option b.

 

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