How do you find the definite integral of #2/(sqrt(x) *e^-sqrt(x))# from #[1, 4]#?
1 Answer
Oct 10, 2016
Explanation:
#I=int_1^4 2/(sqrtx*e^(-sqrtx))dx#
Simplify the negative exponent by bringing it to the numerator.
#I=2int_1^4e^sqrtx/sqrtxdx#
We will use the substitution
#I=4int_1^4e^sqrtx/(2sqrtx)dx=4int_1^2e^udu#
The integral
#I=4[e^u]_1^2=4(e^2-e^1)=4e^2-4e#