Shahd09
Shahd09 Shahd09
  • 02-01-2017
  • Mathematics
contestada

how to integrate ∫㏑x/χ
from 1 to e

Respuesta :

arthurpdc
arthurpdc arthurpdc
  • 03-01-2017
[tex]\int_1^e\dfrac{\ln x}{x}dx,~\text{if}~u=\ln x\to x=e^u\to dx=e^udu\\\\\text{So, finding the new limits:}\begin{cases}x=1\to u=\ln1\to u=0\\x=e\to u=\ln e\to u=1\end{cases}\\\\ \int_1^e\dfrac{\ln x}{x}dx=\int_0^1\dfrac{u}{e^u}e^udu=\int_0^1u\,du=\left[\dfrac{u^2}{2}\right]_0^1=\dfrac{1^2}{2}-\dfrac{0^2}{2}=\dfrac{1}{2}\\\\ \boxed{\int_1^e\dfrac{\ln x}{x}dx=\dfrac{1}{2}}[/tex]
Answer Link

Otras preguntas

Amir bought a camera 5 year ago for RM1500. He plans to sell his camera at a price of RM1800. What percentage of the profit or loss?​
find the missing angles.
I need help:(...pls do it correctly so i could rate u 5 and thank u:)
4. The ratio of skateboards to bikes is 3:1. If there are 12 skateboards, how many bikes are there? A 1 B 2 C3 D4 Answer quick PLZZ no website
Help pls!! What things do babies feel are important?
____________ is refining the extracted raw metals into a purest form
[JAPANESE] Hello, I recently thought of studying Japanese! What is the best way to start learning Japanese? Any tips, etc.? Must know things that I need to lear
coach went and bought 4 bats and 7 baseballs for $68 the next day bought one bat and one ball for 14 how much is each individual item​
which continent in thee eastern hemisphere has mostly young nation​
what are white spot on the nail​