Question

How do you determine the area of a region above the x-axis and below `f(x)=3+2x-x^2`?

Answer 1

`Area=32/3` `u^2`

I would start trying to "see" this area:

So basically you want the area between `x=-1 and x=3` delimited by the curve of equation `f(x)=3+2x-x^2`.
You can use:
`int_(-1)^3(3+2x-x^2)dx=`
`=[3x+x^2-x^3/3]_(-1)^3=`
`=[9+9-27/3]-[-3+1+1/3]=`
`=32/3` `u^2`