用定积分表示直线y=2x与抛物线y=3-x^2在（2,3）上围城成的面积

题目

用定积分表示直线y=2x与抛物线y=3-x^2在（2,3）上围城成的面积

答案

The required area is
∫[2,3] [2x-(3-x²)] dx
= ∫[2,3] (x²+2x-3) dx
= [x³/3+x²-3x] [2,3]
= [3³/3+3²-3*3]-[2³/3+2²-3*2]
= 25/3