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[SOLVED] 4.1.310 AP Calculus Exam find Region

karush

Well-known member
Jan 31, 2012
2,678
310.pngi

Ok this might take a while...
but first find point of intersection $\ln x=5-x$
which calculates to $x=3.69344$ which maybe there is more simpler approach
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
655
this is a calculator active problem ...

$\displaystyle R = \int_1^a \ln{x} \, dx + \int_a^5 5-x \, dx$
where $a$ is the x-value of the intersection.

or ...
$\displaystyle R = \int_0^b (5-y) - e^y \, dy$
where $b$ is the y-value of the intersection.

can you set up the volume by similar cross-section integral ?
 

karush

Well-known member
Jan 31, 2012
2,678
$\displaystyle V = \int_1^a (\ln{x})^2\, dx + \int_a^5 (5-x)^2 \, dx$
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
655
ok ... continue with part (c)
 

karush

Well-known member
Jan 31, 2012
2,678
ok ... continue with part (c)
if we chanhge b to k
$\displaystyle \int_0^k (5-y) - e^y \, dy = \dfrac{1}{2} A$
then solve for k y was derived previous
anyway.....