大一高数定积分题

Question

选择题第一题，怎么做出来的

Answer 1

如图

Answer 2

∫(0->1) f''(x/2) dx^2 =2∫(0->1) x.f''(x/2) dx =4∫(0->1) x.df'(x/2) =4[x.df'(x/2)]|(0->1) -4∫(0->1) f'(x/2) dx =4f'(1/2) -8[f(x/2)]|(0->1) =16- 8[f(1/2) -f(0)] =16- 8(2-1) =16-8 =8