rocksteady
- 3
- 0
Homework Statement
Let f(x) be a continuous function defined on the interval [2, ∞) such that
f(2) = 12
|f(x)| < x^8 + 8
and
⌠∞
f(x) * e^(−x/4) dx = −8
⌡2
Determine the value of
⌠∞
f′(x) * e^(−x/4) dx
⌡2
Homework Equations
The Attempt at a Solution
I started by writing out the integrations. So I have
-4F(∞)e^(-∞/4) + 4(F(2)*e^(-1/2)) = -8
and
-4f(∞)e^(-∞/4) + 4f(2)*e^(-1/2) = ?
I see that I can use f(2) = 12 in the second equation, but I don't see how to use the first equation at all. Nor do I see how |f(x)| < x^8 + 8 can help me. Thoughts?