Question

find the area of the region that is bounded by these equations,,

1) y=lnx, x-axis, x= e^2
2) y = x^2, y = 8-x^, 4x - y +12 =0

Answer 1

have you done integration yet?

Answer 2

not yer

Answer 3

is calculus class?

Answer 4

yes

Answer 5

Then I think only way to solve it is by using integration.
Are you familiar with the concept of integration

Answer 6

yes

Answer 7

So graph two function in calculator. Which one is on top?

Answer 8

you know how ln(x) curve look like. Also x=e^2 is verticle line.

Answer 9

ln(x) is 0 when x=1 right?
so you will \[\int\limits_{1}^{e^2}\ln(x) dx\]

Answer 10

did you get it?

Answer 11

wait

Answer 12

the answer here in the handout is \[e ^2 +1\]

Answer 13

Yes
http://www.wolframalpha.com/input/?i=integral+1+to+e^2%28ln%28x%29+

Answer 14

i got it now... :)

Answer 15

but how can i draw y=lnx and x= e^2 in the cartesian plane

Answer 16

e^2 verticle line

Answer 17

how can i solve for its x and y coordinate?