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(1)
lim(x->0) ∫(0->x) sin(t^2) dt /x^3 (0/0 分子分母分别求导)
=lim(x->0) sin(x^2) /(3x^2)
=lim(x->0) x^2/(3x^2)
=1/3
(2)
f(x) = x(sinx)^2
f(-x) =-f(x)
=>∫(-1->1) x(sinx)^2 dx =0
(3)
∫ (arcsinx)' dx
=arcsinx + C
lim(x->0) ∫(0->x) sin(t^2) dt /x^3 (0/0 分子分母分别求导)
=lim(x->0) sin(x^2) /(3x^2)
=lim(x->0) x^2/(3x^2)
=1/3
(2)
f(x) = x(sinx)^2
f(-x) =-f(x)
=>∫(-1->1) x(sinx)^2 dx =0
(3)
∫ (arcsinx)' dx
=arcsinx + C
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