Question

高数定积分大题

高数定积分大题第二题，求详细过程谢谢🙏
2.题！

Answer 1

∫(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