Question

New question for homework, I would really appreciate the help. I took a screenshot of the problem so it is easier to look at hopefully. I've used up two tries out of five on the first part already while trying to use my notes with a similar problem, but it didn't work out. https://gyazo.com/3e5e111b532f5afc1a687d4efc326465

Update: I figured out part b to be 9. Don't know why it took me so long to figure that out. I still need help for part a, though.

Answer 1

(a)

Let u = t/6
so du = dt/6 --> dt = 6du


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endpoints (ie limits of integration)
if t = 0, then
u = t/6
u = 0/6
u = 0


if t = 36, then
u = t/6
u = 36/6
u = 6


so the limits t = 0 to t = 36 become u = 0 to u = 6

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\[\Large \int_{0}^{36} g\left(\frac{t}{6}\right)dt = \int_{0}^{6}g(u)(6du)\]

\[\Large \int_{0}^{36} g\left(\frac{t}{6}\right)dt = 6\int_{0}^{6}g(u)du\]

\[\Large \int_{0}^{36} g\left(\frac{t}{6}\right)dt = ???\]

Answer 2

Hmm... well, from that second equation, it looks like it ends up essentially being 6*9 = 54. Is it really that simple? I feel slightly embarrassed now.

Answer 3

yeah part (a) is 54

Answer 4

Alright, that was quick. Thanks for the help.

Answer 5

no problem