Question

高中数学 请问怎么做 着急在线等

Answer 1

设f(x)=ax+b
∫(0,1)f(x)dx=5
∫(0,1)(ax+b)dx=5
[(a/2)x^2+bx]|(0,1)=5
(a/2)1^2+b×1-[(a/2)×0^2+b×0]=5
a/2+b=5
a+2b=10.......(1)
∫(0,1)xf(x)dx=17/6
∫(0,1)x(ax+b)dx=17/6
∫(0,1)(ax^2+bx)dx=17/6
[(a/3)x^3+(b/2)x^2]|(0,1)=17/6
(a/3)×1^3+(b/2)×1^2-[(a/3)×0^3+(b/2)×0^2]=17/6
a/3+b/2=17/6
2a+3b=17.......(2)
联解(1)(2)：a=4，b=3
f(x)=4x+3
∫(1,2)f(x)/xdx
=∫(1,2)(4x+3)/xdx
=∫(1,2)(4+3/x)dx
=(4x+3lnx)|(1,2)
=4×2+3ln2-(4×1+3ln1)
=8+3ln2-4-0
=4+3ln2