Question

Let f(x)be a continuous function defined on the interval [2, infinity) such that
f(4)=14
|f(x)| < x^3+10
and
the integral from 4 to infinity f(x)*e^(-x/4) = -5
Determine the value of:
the integral from 4 to infinity f'(x)*e^(-x/4) = ?

Answer 1

Use integration by parts.

Answer 2

hey... double post.

Answer 3

u = f(x) dv = e^(-x/4)
du = f'(x) v = -4e^(-x/4)

--> -4f(x)e^(-x/4) +4* integral f'(x)e^(-x/4)
evaluate from 4 to infinity
--> (56/e) +4* integral f'(x)e^(-x/4) = -5

--> integral f'(x)e^(-x/4) = (-5e -56)/4e