Find the values of a and b which make

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

as large as possible.

Question

Find the values of a and b which make

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

as large as possible.

nowhereman · Answer

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

jamesj · Answer

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.

nowhereman · Answer

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

jamesj · Answer

yes, good point.

anonymous · Answer

|dw:1323754321936:dw| 
what we have here is a negative parabola the crosses the x-axis at (-)1 and (+)2

anonymous · Answer

|dw:1323754912753:dw|