Question

i will give medals if anyone can solve this question or at least attempt it!!

Answer 1

Let 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 2

I=\[\int\limits_{4}^{infity}( f(x)*e^(-x/4))\]=-5.
I'=\[\int\limits_{4}^{infity}( f'(x)*e^(-x/4))\]=X(let)
I+I'=\[\int\limits_{4}^{infity}( f(x)*e^(-x/4))\]+\[\int\limits_{4}^{infity}( f'(x)*e^(-x/4))\]
-5+X=-4*([f(x)*e^x](from -1 to -infinity))=>-5+x=(56/e)=>X=(56/e)+5.....