evaluate:

Question

evaluate:

megannicole51 · Answer

$$\int\limits_{0}^{1} \int\limits_{e ^{y}}^{e} \frac{ 1+e ^{x} }{ \ln(x) }dxdy$$

megannicole51 · Answer

@agent0smith

hartnn · Answer

so are you taught change of order ?

agent0smith · Answer

$$\Large \int\limits\limits_{0}^{1} \int\limits\limits_{e ^{y}}^{e} \frac{ 1+e ^{x} }{ \ln(x) }dxdy$$ cos it's easier to read

megannicole51 · Answer

$$\int\limits_{e ^{y}}^{e}\frac{ 1+e ^{y} }{ \ln(x) }dx$$

megannicole51 · Answer

first?

megannicole51 · Answer

no bc my professor is incompetent

megannicole51 · Answer

please teach me

hartnn · Answer

yeah, thats the problem, that function cannot be integrated
thats where change of order comes into picture

megannicole51 · Answer

how do u know that

agent0smith · Answer

$$\Large \int\limits\limits_{e ^{y}}^{e}\frac{ 1+e ^{y} }{ \ln(x) }dx$$above it was a 1+e^x now it's 1+e^y...?

hartnn · Answer

wait what ?

megannicole51 · Answer

its x sorry i messed up

hartnn · Answer

ok, we can use change of order when
1) the function to be integrated is very difficult to integrate
2) or its not possible to integrate in standard functions

we'll know this only by trying it out

hartnn · Answer

if you want to make sure, try it out by whichever formulas you know. 
if you find it difficult/impossible , you'll then appreciate the use of change of order

primeralph · Answer

Why bother? Just use the bounds to bind the integral.

hartnn · Answer

the first step for changing the order will be to find the region
the limits are 
x = e^y to x =e 
can you plot these 2 curves ? 
(x= e will be a line)

megannicole51 · Answer

theres not an easier way to do this? on my exam i wont be able to plot the curves bc i cant do it offhand

hartnn · Answer

if change of order is involved, getting the region of integration is must.

megannicole51 · Answer

lovely:(

primeralph · Answer

Or get a really cool calculator.

megannicole51 · Answer

no calculators can be used for college exams.

megannicole51 · Answer

i never use mine anymore

isaiah.feynman · Answer

Your brain will bud. :)

megannicole51 · Answer

okay im not trying to be mean but my calc final is monday. @hartnn can we get back to the problem i really just need to know how to do it step by step.

hartnn · Answer

you can plot x= e^y by hand ?

hartnn · Answer

x= e is easy,

megannicole51 · Answer

no i can't but i can look it up

dan815 · Answer

|dw:1387090843328:dw|