Thread: integrals

1. integrals

what if x appears inside the integral?
find f'(x) for f(x) = integral from a to b of g(x,t) dt

and then

use this result to evaluate I= integral from 0 to 1 of (t^2)*(e^(-t)) dt
and they give you a hint which makes no sense to me

Hint: Compute integral from 0 to 1 of e^(-st) dt
where s is a parameter
How is I related to this integral?

2. Originally Posted by razorfever
what if x appears inside the integral?
find f'(x) for f(x) = integral from a to b of g(x,t) dt

and then

use this result to evaluate I= integral from 0 to 1 of (t^2)*(e^(-t)) dt
and they give you a hint which makes no sense to me

Hint: Compute integral from 0 to 1 of e^(-st) dt
where s is a parameter
How is I related to this integral?
I think this is what there getting at.

If $\displaystyle (1)\;\;\;g(s) = \int_0^1 e^{-st}\,dt$ then

$\displaystyle g''(s) = \int_0^1 t^2 e^{-st}\,dt$

and
$\displaystyle g''(1) = \int_0^1 t^2 e^{-t}\,dt$ your integral. Now from (1), integrate to find $\displaystyle g(s)$ differentiate twice and evaluate at $\displaystyle s = 1$.