VCAA Question - PLEASE HELP!

[DylanBurrowes]

I'm really struggling with VCAA Exam 2 2010 MC Q20.

No idea how to do these sorts of questions. Any help is greatly appreciated!

[1001]

define  f(x)=1 on your calc. It will be easy after that.

[DylanBurrowes]

Woah, thanks so much! But still doing that work in every type of these questions?

[Rectophobia]

With these kinds of questions, it's important to have a visual representation of how the curve is shifted. Firstly, separate the integral into its two components (2[∫f(x/5)·dx + ∫(3)·dx])  and then evaluate them individually.
For the +3 part, you can just substitute the given values from the terminals and evaluate.

2∫(3)·dx (between 0 and 5a) = 30a

Then for the second part, f(x/5), the graph is dilated by 5 in the x-direction (which essentially means that the area under f(n) will be 5 times larger). In this case, n = 5a/5 = a. We already know that ∫f(x)·dx between 0 and a = a; so 2∫f(x/5)·dx between 0 and a = 5a is 10a

=> 2∫f(x/5)+3·dx = 40a

[teexo]

what does define f(x) = 1 do? sorry I'm really confused by these types of questions

[DylanBurrowes]

Thanks so much!!

[Twanny666]

Literally just did this exam,
This is the only sort of question I always refer to my bound book when doing.
I have a summary for it that pretty much allows me to do it..
This was my best exam yet... got 79/80...