SOLUTION: Find the area between the two curves f(x)=1/(x+2) and g(x)=e^x over the interval [0,1] Please help!!!

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Question 64322: Find the area between the two curves
f(x)=1/(x+2) and g(x)=e^x
over the interval [0,1]
Please help!!!
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Find the area between the two curves 
f(x)=1/(x+2) and g(x)=ex 
over the interval [0,1] 

 

ó1	
ô(yupper green curve - ylower red curve)dx 
õ0

ó1	
ô[g(x) - f(x)]dx = 
õ0

ó	
ô[ex - 1/(x+2)]dx
õ
             |1
ex - ln|x+2| |  = [e1 - ln|1+2|]-[e0 - ln|0+2|] =
             |0

[e - ln(3)] - [1 - ln(2)] = e - ln(3) - 1 + ln(2) =

ln(2) - ln(3) + e - 1 = ln(2/3) + e - 1 = 1.31281672

Edwin
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