00:01
Question wants us to use our rules of integration that we know to evaluate four different integrals.
00:06
So if we start with a, we see that we're given 0 to negative 3 g of t, dt.
00:14
And we should know from our rules that if we flip the order of the bounds of integration, all we do is negate our answer.
00:21
So since we have negative 3 to 0 originally, but now we have 0 to negative 3, our answer is negative root 2.
00:28
Part b, we're given negative.
00:30
3 to 0, g of u, du.
00:34
Because all we did was switch the variable.
00:38
That makes no change to the integral itself.
00:43
So this is still root 2 because u here and t are just temporary variables.
00:50
And if we switch it to m, z, whatever, it doesn't matter.
00:53
The integral is still the same.
00:54
So root 2.
00:55
C says 0 to, oh sorry, negative 3 to 0, there you go, of negative g of x, dx, and again, the variable change doesn't make a difference.
01:13
We just ignore that.
01:15
What does matter is this negative sign...