Evaluating an integral with pi

[twinmom]

I'm confused as to how to evaluate the integral pi/x and evaluate from 1 to e. Should I use substitution and make u=x? If so, then how does pi calculate during the evaluation?

 

[galactus]

Pi is a constant. You can take it outside the integral sign.

\(\displaystyle \L\\{\pi}\int_{1}^{e}\frac{1}{x}dx\)

Do you know what the integral of 1/x is?. Once you see that it's easy as pi.

 

[tkhunny]

...how does pi calculate during the evaluation?

I often wonder why this is such a common question. \(\displaystyle \pi\) is a number. I think it's the teacher's fault. Would you be confused if it were 4/x? So many teachers and textbooks fail to teach similarity and consistency. How about \(\displaystyle \sqrt{2}\)/x? They would rather teach that every slight variation is an entirely new problem. You don't seem to have a problem with 'e' or '1'. But that's just my opinion.

 

[twinmom]

Thank you; yes I can take it from here. You guys are great!!