AP Calculus Testbank

AP Calculus Testbank
(Chapter 6)
(Mr. Surowski)

Part I. Multiple-Choice Questions


∫1
1. Suppose that f is an odd differentiable function. Then xf r(x) dx =
—1

(A) f (1);
(B) fr(1)
(C) f (1) — f (—1)
(D) 0
(E) 2.


2. The slope field indicated below most likely depicts the differen-
tial equation

dy
(A) =x+y
dx
dy
(B) =x+5
dx
dy
(C) =y+5
dx
dy
(D) = —x + 5
dx
dy
(E) = —y + 5
dx

,3. You are given differentiable functions f and g. Which of the
following is a consequence of the integration by parts formula?
∫ ∫
(A) frr(x)g(x) dx + f (x)grr(x) dx = fr(x)gr(x)
∫ ∫
(B) frr(x)g(x) dx + fr(x)gr(x) dx = f (x)g(x)
∫ ∫
(C) frr(x)g(x) dx + fr(x)gr(x) dx = fr(x)g(x)
∫ ∫
(D) frr(x)g(x) dx + f rrr(x)g(x) dx = fr(x)g(x)
∫ ∫
(E) frr(x)g(x) dx + f (x)gr(x) dx = f (x)g(x).


4. Given the slope field below, what is the most plausible behavior
dy
of the solution of the IVP = f (x, y), y(—4) = 4?
dx
(A) lim y = —∞
x→∞
(B) lim y = 0
x→∞
(C) lim y = +∞
x→∞
(D) lim y = does not
x→∞
exist.
(E) lim y = —2
x→∞



dy 1√
5. You are given the differential equation = — y, where y(0) =
dx 5
25. For which value(s) of x is y = 0?
(A) ±5 (B) 10 (C) 50 (D) ±10 (E) 5

, ∫
6. tan6 x sec2 xdx =

tan7 x
(A) +C
7
tan7 x sec3 x
(B) 7 + +C
3
tan7 x sec3 x
(C) 21 +C
(D) 7 tan7 x + C
2
(E) tan7 x sec x + C
7

∫ 1/2
2
7. √ dx =
0 1 — x2
π π π 2π 2π
(A) (B) (C) — (D) (E) —
6 3 3 3 3

∫
2
8. 7xe3x dx =

1
(A) e3x + C
2

42
6 3x2
(B) e + C
7
7 2
(C) e3x + C
6
2
(D) 7 e3x + C
2
(E) 42 e3x + C