For x>0, define L(x)=∫1x​t1​dt. (keep in mind that we require x be positive so that the FTC applies and the function, L(

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For X 0 Define L X 1x T1 Dt Keep In Mind That We Require X Be Positive So That The Ftc Applies And The Function L 1 (35.61 KiB) Viewed 37 times

For x>0, define L(x)=∫1x​t1​dt. (keep in mind that we require x be positive so that the FTC applies and the function, L(x), is both continuous and differentiable). Using this definition and properties of the integral prove the following: a. L(1)=0. b. L′(x)=x1​ for every x>0. c. L(ab)=L(a)+L(b) for every a,b>0.