In general:
But because they're definite integrals it can be useful to calculate them.
So is this true then?
1.
Let so that
Then
2.
Let and so that
Then
Seems correct, but it seems too simple. I suppose these problems could be just to illustrate how integration and differentiation are inverse processes.
Since Plato edited his response to include the above, it appears at least one of my answers is wrong.
2.
Let and so that
Also, if and then this would conform with Plato's formula and the derivatives would be .
The integral would NOT be what I posted earlier: .
Instead, this is what I'm thinking:
Because the derivative of is 1, I'm sticking with my original results for the first problem, which was
Once again, can anyone confirm or deny these answers? Thanks.