suppose ∫f(t)dt (from 0 to 1)=3. calculate the following:
∫f(2t)dt (from 0 to 0.5)
∫f(1-t)dt (from 0 to 1)
∫f(3-2t)dt (from 1 to 1.5)

Question

suppose  ∫f(t)dt (from 0 to 1)=3. calculate the following:
 ∫f(2t)dt (from 0 to 0.5)
 ∫f(1-t)dt (from 0 to 1)
 ∫f(3-2t)dt (from 1 to 1.5)

anonymous · Answer

I'm not sure how to explain this, it's a bit of a trick question. If you look closely you can see that those three integrals are all really the same as $\int_0^1f(t)dt$. First they tranform inside f, only to undo it with the integration boundaries.

anonymous · Answer

So for the first one, 2t for t between 0 to 0.5 is really the same as t for t between 0 and 1.

anonymous · Answer

In both cases you get all the points between 0 and 1.

anonymous · Answer

so they all equal 3?

anonymous · Answer

That's right.

anonymous · Answer

can you show me how to do it?

anonymous · Answer

Like I said, I'm having a tough time explaining this, I don't think I can do any better than I already did, sorry.

anonymous · Answer

thanks