Question

Which of the following integrals represents the area of the region bounded by x = e and the functions f(x) = ln(x) and g(x) = log1/e(x)?

Answer 1

@pooja195

Answer 2

@johnweldon1993

Answer 3

hi you got any ideas?

Answer 4

hey

Answer 5

have you tried to graph that

Answer 6

yes I dd

Answer 7

you need to know what function is larger than the other

Answer 8

so what did you got

Answer 9

so you are taking area from 1 to e
you need to split that int

Answer 10

no split sorry

Answer 11

just think of what function is above and which is below

Answer 12

taking from 0 to e is not possible that is a defined area especially from 0 to 1

Answer 13

is not a defined area *

Answer 14

so then i know it's not C

Answer 15

option C ? you sure

Answer 16

If it's from 1 to e it must be either B or D right?

Answer 17

oh i see i miss read your comment lol

Answer 18

yeah either of those

Answer 19

so the function that is above will come first correct?

Answer 20

yes

Answer 21

The regions above and below the x-axis have area equivalent in magnitude. So in case you wanted to calculate the integral, ....

Answer 22

we are not interested on the value do we?

Answer 23

no we don't need to know the value

Answer 24

alright!

Answer 25

is f(x) = ln(x) the function that is above. thats what it look like on my graph

Answer 26

this integral technically speaking we are setting a net area not area

Answer 27

yeah

Answer 28

sooo it would be D? Right?

Answer 29

yes

Answer 30

Yay! Thank you :)

Answer 31

no problem :)

Answer 32

This is just a side note really

Using the change of base rule, we can say

\[\Large \log_{1/e}(x) = \frac{\log(x)}{\log(1/e)}\]

\[\Large \log_{1/e}(x) = \frac{\log(x)}{\log(e^{-1})}\]

\[\Large \log_{1/e}(x) = \frac{\log(x)}{-1*\log(e)}\]

\[\Large \log_{1/e}(x) = -1*\frac{\log(x)}{\log(e)}\]

\[\Large \log_{1/e}(x) = -1*\ln(x)\]

\[\Large \log_{1/e}(x) = -\ln(x)\]


so instead of saying \(\Large \log_{1/e}(x)\), you can say \(\Large -\ln(x)\)


For some reason, your teacher didn't make this conversion

Answer 33

i thought of change of base but somehow i ignored that
from the graph you can tell that's -lnx