Explain why the two integrals are equal:
All I was able to work out is the two original functions:
Looking at a graphing calculator, I can see the similarities, but I don't know how to articulate them mathematically.
I think so, but for some reason I still don't see where this is going. I'm returning to calculus after being out of it since last May, so that might be the reason for my not understanding this right away.
The integration by substitution I remember looked something like this:
Where u would be, I guess, e^t, and du would be e^t, but that doesn't help solve at all and even doesn't work because you can't divide by e^t outside the integral. (So obviously I don't understand what's being suggested here.)
.
Substitute .
Then:
1. .
2. and .
3. .
Then .
But since it's a definite integral, u is just a dummy variable and you can replace the symbol u with the symbol x.
You need to thoroughly review and revise how to integrate because your instructor obviously assumes you know how to do things like this (otherwise you would not be asked to do questions like this). And most likely you need to review basic algebra (such as index laws etc.) too.