Question

Integral help please!

Answer 1

Suppose \[\int\limits_{0}^{2}g(u)du=12\]
Evaluate the following:
\[\int\limits_{0}^{4}g(t/2)dt\]
\[\int\limits_{0}^{2}g(2-t)dt\]

Answer 2

\[\int_0^4 g(t/2)~dt\]
Let \(u=t/2~\Rightarrow~2~du=dt\).
The limits change to (upper) \(u=4/2=2\) and (lower) \(u=0/2=0\).
\[\frac{1}{2}\int_0^2 g(u)~du\]

Answer 3

So that would be 6 then?

Answer 4

Yes

Answer 5

How would I set up the second one?

Answer 6

For the second one, let \(u=2-t~\Rightarrow~-du=dt\).
Limits change to (upper) \(u=2-2=0\) and (lower) \(u=2-0=2\).
\[-\int_2^0 g(u)~du=\int_0^2 g(u)~du\]

Answer 7

Oh, okay.
It there something I am missing in the first one? 6 should not be the answer.

Answer 8

Oh sorry, that should be a 2, not 1/2 out front. My bad

Answer 9

It's okay. Thank you for all of your help!

Answer 10

You're welcome!