1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

İnfinite İntegral Area

  1. Mar 8, 2017 #1
    1. The problem statement, all variables and given/known data
    Find the area Below ##y=0##,above ##y=lnx##, and to the right of ##x=0##

    2. Relevant equations


    3. The attempt at a solution
    I thought an integral like ##\int_0^1 lnx \, dx##
    then Its ##-∞## at ##x=0## So I used like ##lim(a→0)=\int_a^1 lnx \, dx## and from that it came
    The integral result is ##xlnx-x## so ##1(ln1-1)-a(lna-1)## And if we take limit first term ##1(ln1-1)## is ##-1## but the other term bothers me.It will be ##0(-∞-1)##. I can think like ##lim (a→0)=a ln(a)## and that gave me ##0## but theres also ##+1## so the answer turns ##0## but its impossible.Where I am doing wrong ?
     
  2. jcsd
  3. Mar 8, 2017 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    $$ \int_a^1 \ln x \, dx =\left. x \ln x -x \right|_a^1 = 1 \ln 1 - 1 - a \ln a + a$$
    What is the limit of that as ##a \to 0+##?

    BTW; do not write ##ln x##-- it is ugly and hard to read; instead, write ##\ln x##. You do that by typing "\ln" instead of "ln". (Same for "log", "exp", "lim", "max", "min", all the trig functions and their inverses, and the hyperbolic functions---but not their inverses.)
     
  4. Mar 8, 2017 #3

    fresh_42

    Staff: Mentor

    Which area is described by the given conditions? Draw a picture of it or describe it with words.
     
  5. Mar 8, 2017 #4
    oh ok I foıund thanks
     
  6. Mar 8, 2017 #5

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I doubt you have found the correct answer since your original integral is wrong. Remember area is$$
    \int_a^b y_{upper} - y_{lower}~dx$$which is not what you have in your integrand.
     
  7. Mar 8, 2017 #6
    Well that make sense...Hmm...ok thanks
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: İnfinite İntegral Area
  1. Integral and area (Replies: 4)

  2. Area Integral (Replies: 1)

  3. Infinite integral (Replies: 2)

  4. Infinite Integral (Replies: 2)

  5. Integration - areas (Replies: 7)

Loading...