___________________________________________________________________
Calculus  II                                              Test #3                                   April 19, 2004

Name____________________         R.  Hammack                               Score ______
___________________________________________________________________

(1) Find the following integrals.

(a) ∫  1/(4 - x^2)^(1/2) dx =


(b) ∫  tan^2(x) dx =


(c) ∫  x sin(5x) dx =



(d) ∫  sin(ln(x))   dx =



(e)  ∫_0^( π/2) cos^3(x) dx =


(f)  ∫  tan^2(x) sec^2(x)   dx =



(g)  ∫    (9 - x^2)^(1/2) dx =   




(h)  ∫ (x^2 - 1 )^(1/2)/x   dx =




(i) ∫ (2x + 10)/(x^2 + 10x + 24)   dx =



(j) ∫   (x^2 + 2)/(x + 2)   dx =



(2) Evaluate the following improper integrals.

(a)   ∫_2^∞2/x^2 dx =


(b)   ∫_0^1x^(-1/3) dx =


(3) Evaluate the limits.

(a) Underscript[lim , x⟶0^+] ln(x)/(x - 1) =


(b)   Underscript[lim , x⟶∞] (1 - 3/x)^x =