BC Calculus ‘14
Integration Techniques Test
name
Score
1.
1
⌠
dx =
⎮ 2
⌡ x − 6x + 8
(a)
1 x−4
ln
+c
2 x−2
(d)
⌠ x−3
dx =
⎮
⌡ x
(a)
1− 3ln x + c
(d)
(b)
3x 2
⌠
dx =
⎮ 2
⌡ x + 3x + 2
(a)
2
x + 2)
(
ln
( x + 4)
(d)
+c
2
x + 2)
(
2 ln
x +1
(e)
(c)
1
ln ( x − 4 ) ( x − 2 ) + c
2
ln ( x − 4 ) ( x − 2 ) + c
x − 3ln x + c
x 2 − 3x
+c
x2
3.
1 x−2
ln
+c
2 x−4
1
ln ( x − 4 ) ( x + 2 ) + c
2
2.
(b)
(e)
(c)
1+
3
+c
x2
1 2
x − 3ln x + c
2
(b)
x +1
ln
+ c (c)
x+2
+c
(e)
2
x + 1)
(
ln
x+2
+c
None of these
1
4.
∫0 x tan
(a)
π
4
−1
x dx =
(b)
(c)
π
2
(d)
π −2
2
(e)
π −2
4
π
2 e x cos x dx
0
5.
∫
(a)
1 π /4
( e + 1)
2
(d)
π −2
=
(b)
1 π /2
( e + 1)
2
1 π /4
( e − 1)
4
(e)
(c)
1 π /2
( e − 1)
2
1 π /2
( e + 1)
4
dP
, of the number of people on a particular beach is
dt
modeled by a logistic growth equation. The maximum number of people on the
beach is 1200. At 10:00 am, the number of people on the beach is 200 and the rate
is increasing at 400 people per hour. Which of the following differential equations
models the situation?
6.
The rate of growth,
(a)
dP
1
=
(1200 − P ) + 200
dt 400
dP 2
= (1200 − P )
dt 5
dP
1
=
P (1200 − P )
dt 500
dP
1
=
P (1200 − P )
dt 400
dP
= 400P (1200 − P )
dt
(b)
(c)
(d)
(e)
−2x 3
7.
, x = 1 , x = 2 , and the x-axis. Find
2x 2 + 7x + 3
the volume of a solid where R is the base of the solid and the cross-sections
perpendicular to the x-axis are isosceles right triangles with one leg in region R.
Show the anti-differentiation. A region R is bounded by y =
8.
−1
2
∫ 2x sin ( x ) dx