# Math Help - def integral with substitution

1. ## def integral with substitution

Suppose
Evaluate the following

(b)

Im still feeling a little lost...I'm not sure on when to change the limits, and if du= -dt do i inverse the u? Thanks for all the help!

2. Originally Posted by gabet16941
Suppose
Evaluate the following

(b)

Im still feeling a little lost...I'm not sure on when to change the limits, and if du= -dt do i inverse the u? Thanks for all the help!
Let $u = 6 - t$

$\Rightarrow du = -dt \implies -du = dt$

change the limits:

$t = 6 \implies u = 0$
$t = 0 \implies u = 6$

so our integral becomes:

$- \int_6^0 g(u)~du = \int_0^6 g(u)~du = 6$