How do you evaluate the definite integral #inte^(lnx+2)# from #[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 ... #
