Question

高数题，求解鸭！

做出来了，答案不确定。所以来对一下

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Answer 1

详情如图所示

有任何疑惑，欢迎追问

Answer 2

(13)

f(x)=∫(0->x) xsin(t^2) dt
=x∫(0->x) sin(t^2) dt
f'(x)=∫(0->x) sin(t^2) dt + xsin(x^2)
(11)
f(x) = 1/(1+x^2) + x^2.∫(0->1) f(x) dx
let
C=∫(0->1) f(x) dx
f(x) = 1/(1+x^2) + x^2.∫(0->1) f(x) dx
∫(0->1) f(x) dx=∫(0->1) [1/(1+x^2) + Cx^2 ] dx
C = [ arctanx +(1/3)Cx^3]|∫(0->1)
= π/4 + (1/3)C
(2/3)C=π/4
C =3π/8
=> ∫(0->1) f(x) dx =3π/8