Question

Find the values of a and b which make

\[\int\limits_{a}^{b}(2+x-x ^{2}) dx\]

as large as possible.

Answer 1

You can calculate the value of this integral depending on a and b explicitly, then maximize that new expression.

Answer 2

Before you do that though, I recommend drawing a graph of the integrand and asking yourself what you expect the answer to be. I think you'll find it's pretty straightforward.

Answer 3

I guess it's under the condition that \( a < b \) or else it won't be bounded.

Answer 4

yes, good point.

Answer 5

what we have here is a negative parabola the crosses the x-axis at (-)1 and (+)2