Math 126-101 CRN 31611
Carter
Sample Test 1 Spring 2016
General Instructions. Do not write upon this test sheet. Write your name on only the
outside front cover of your blue book. Write all of your solutions neatly and clearly inside
your blue book. You do not need to do the problems in the order that I suggest here, but
I recommend doing so. You should, however, label your problems carefully, and make sure
that the problem upon which you are working is made clear. There are problems on the
front and back of this sheet. The test is worth 108 points.
Meanwhile, be willing to experiment with food flavors. A bit of sesame oil, some soy
sauce, sugar, lemon, and mayonnaise makes a nice Asian flavored salad dressing.
1. (10 points) Use the fundamental theorem of calculus to compute
Z x√
d
1 + t3 dt
dx 0
2. Compute the following definite and indefinite integrals (8 points each).
(a)
4
Z
3x2 − 4x + 5 dx
1
(b)
Z
3
x2 ex dx
(c)
Z
√
x
dx
1 + x2
(d)
Z
π/2
cos (x) dx
π/6
(e)
Z
√
(1 + x)4
√
dx
x
(f)
Z
(2x + 1) sin (x2 + x) dx
1
3. (10 points) Compute the area that lies between the curve y = x3 − x and the x-axis
for −1 ≤ x ≤ 1.
4. (10 points) Determine the volume that is obtained by revolving the region that is
bounded by the curves x = y 2 , y = 0, and y = 3 about the x-axis.
p
Rb
5. (10 points) Use the surface area formula S = a 2πf (x) 1 + (f 0 (x))2 dx to compute
the lateral surface area of the cone y = x/2 for 0 ≤ x ≤ 4 about the x-axis.
6. (10 points) Determine the area of the bounded region between the curves y = x2 and
y = x + 2.
7. (10 points) A rope that weights 0.08 pound per foot is lifted 20 feet from the edge of
a cliff. How much work (measured in foot pound) is done in lifting the rope?
2