How do you evaluate the definite integral inte^(lnx+2)∫elnx+2 from [1,2][1,2]?
1 Answer
May 9, 2018
int_1^2 \ e^(lnx+2) \ dx = (3e^2)/2
Explanation:
We seek:
I = int_1^2 \ e^(lnx+2) \ dx
Using the properties of exponents:
I = int_1^2 \ e^(lnx)e^(2) \ dx
\ \ = e^2 \ int_1^2 \ x \ dx
Which we can readily integrate using the power rule, so that:
I = e^2 \ [ x^2/2 \ ]_1^2
\ \ = e^2 (4/2-1/2)
\ \ = (3e^2)/2
\ \ ~~ 11.083584 ...