How do you find the definite integral of 2/(sqrt(x) *e^-sqrt(x)) from [1, 4]?

1 Answer
Oct 10, 2016

4e^2-4e

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 u=sqrtx. This implies that du=1/(2sqrtx)dx. Don't forget to plug the bounds of 1 and 4 into sqrtx.

I=4int_1^4e^sqrtx/(2sqrtx)dx=4int_1^2e^udu

The integral inte^udu=e^u+C:

I=4[e^u]_1^2=4(e^2-e^1)=4e^2-4e