高数定积分第4题

高数定积分第4题求详细步骤谢谢俶
2025-03-10 11:48:23
推荐回答(1个)
回答1:

∫(0->x^2) f(t) dt = lnx + 1/x
两边求导
2x.f(x^2) = 1/x - 1/x^2
x=2
4f(4) = 1/2 -1/4
f(4) = 1/16
//
2x.f(x^2) = 1/x - 1/x^2
两边求导
2[ f(x^2) - 2x^2.f'(x^2) ] = -1/x^2 + 2/x^3
x=2
2[ f(4) - 8f'(4) ] = -1/4 + 2/8
2( 1/16 -8f'(4) ) = 0
f'(4) = 1/128