Shahd09
Shahd09
02-01-2017
Mathematics
contestada
how to integrate ∫㏑x/χ
from 1 to e
Respuesta :
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
VER TODAS LAS RESPUESTAS ( 16+ )
Otras preguntas
The discovery of Hammurabi's law code was an important archaeological find because it __________. was the first law code developed in the Middle East showed tha
If you broke a piece of matter into its smallest components, you would be left with ______________. A.) molecules B.) cells C.) protons D.) atoms
The middle layer of the urinary bladder is identified as ___________. a. Mucous coat b. Submucous coat c. Muscular Coat d. Sphincter Coat
What is the appropriate term to describe the triangular-shaped mouth of the Nile River?
1). [(6,1), (6,2), (6,3)] 2). [(0,5), (5,-1), (5,9)] 3). [(1,-6), (3,-5), (1,0)] 4). [(0,8), (1,7), (2,6)]. Which of the following relations is a function?
Tamara bought one quart of juice. She drank one pint of juice. How many cups are left?
Which of the following believed that people would respond if there were clear rewards or punishments for their actions? a. Confucius b. Laozi c. Han Fei Tzu
Which of the following believed that people would respond if there were clear rewards or punishments for their actions? a. Confucius b. Laozi c. Han Fei Tzu
how do you write 26.17 in word form
What is one reason there were few Dutch immigrants in the Middle Colonies before 1800? Select the best answer from the choices provided. 1.The number of German
