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[SOLVED] 4.1.310 AP calculus Exam Area under to functions

karush

Well-known member
Jan 31, 2012
2,678
Capture.PNG
ok I got stuck real soon.....

.a find where the functions meet $$\ln x = 5-x$$
e both sides
$$x=e^{5-x}$$


ok how do you isolate x?

W|A returned $x \approx 3.69344135896065...$
but not sure how they got it


b.?
c.?
 
Last edited:

skeeter

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

$y = \ln{x} \implies x = e^y$

$y = 5-x \implies x = 5-y$

\(\displaystyle R = \int_0^{1.3065586} (5-y) - e^y \, dy = 2.986\)
 

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karush

Well-known member
Jan 31, 2012
2,678
so then we don't need to know x of the intersection
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
655
so then we don't need to know x of the intersection
yes, you need both x and y coordinates of the intersection point ...

(a) can be done w/r to x or y ... I went w/r to y because it only requires a single integral expression

(b) requires x ... two integrals

(c) requires y
 

karush

Well-known member
Jan 31, 2012
2,678
ill go with c
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
655