Question

定积分求解 详细过程

过程详细点

Answer 1

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追答

Answer 2

(1)
∫(0->2) f(x) dx
=∫(0->1) f(x) dx + ∫(1->2) f(x) dx
=∫(0->1) 3x dx + ∫(1->2) (2x-1)^2 dx
=(3/2)[x^2]|(0->1) + (1/6)[ (2x-1)^3]|(1->2)
=3/2 +(1/6)( 27 - 1)
=3/2 + 26/6
=35/6
(2)
∫(-1->2) |x-1| dx
=-∫(-1->1) (x-1) dx + ∫(1->2) (x-1) dx
= [-(1/2)x^2 + x ]|(-1->1) + (1/2)[ (x-1)^2]|(1->2)
= ( 1/2 + 3/2) + (1/2) ( 1-0)
= 5/2
(3)
let
f(x)= x^2. sinx
f(-x) = -f(x)
∫(-1->1) x^2.(sinx +1) dx
=∫(-1->1) x^2 dx
= (1/3)[x^3]|(-1->1)
=2/3

追问

第一题为什么变成六分之一了 不是应该三分之一吗 求教