Question

求大神解高数，有图片。感谢

方便的话写在纸上拍照发给我，谢谢

Answer 1

以上，请采纳。

Answer 2

(1) 令 √(1+lnx) = u, 则 x = e^(u^2-1), dx = 2ue^(u^2-1)du
I = ∫<下1, 上√3>2ue^(u^2-1)du/[ue^(u^2-1)]
= ∫<下1, 上√3>2du = 2(√3-1).
(2) I = [xarcsinx]<0, 1> - ∫<0, 1> xdx/√(1-x^2)
= π/2 + (1/2)∫<0, 1> d(1-x^2)/√(1-x^2)
= π/2 + [√(1-x^2)]<0, 1> = π/2 - 1.
(3) 令 ∫<0, π>f(x)cosxdx = A, 则 f(x) = x-A,
f(x)cosx = (x-A)cosx, 两边在[0, π]上积分得
A = ∫<0, π>(x-A)cosxdx = ∫<0, π>(x-A)dsinx
= [(x-A)sinx]<0, π> - ∫<0, π>sinxdx
= 0 + [cosx]<0, π> = -2, 则 f(x) = x+2