Different result from Integrate and NIntegrate?

Questions
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1

Hello everyone,

I am trying to acquire the solution (A) to an integral and subsequently numerically integrate Exp[-A]. However, I get a different answer depending on whether I solve for A analytically or numerically. I am hoping to find a way to solve for A numerically but get the same numerical solution to Exp[-A] as I would if I solved for A analytically. Is this possible?

Question.nb (7.59 KB)

2

See attached file:

Question A.nb (14 KB)

3

Thank you SO much!! I knew I was doing something wrong.