96年 - 96 國立政治大學轉學生招生考試_應用數學系：微積分(二)#122392

(1) Compute the volume of the solid enclosed by the ellipsoid= 1, where a, b, c are positive constants. (15%)

(2) Let f(x) and g(x) be two continuous real-valued functions on [a,b]. Show that |(f(x)g(x))dx|² ≤ ((|f(x)|²dx))((|g(x)|²dx). (15%)

(3) Evaluate the improper integral dx if exists. (10%)

(a) ∫ln xdx

(b) ∫sec xdx

(a) if exists

(b)dt if exists

(c) if exists