Math 126-101 CRN 31611
Carter
Sample Test 1 Spring 2016
1. (10 points) Use the fundamental theorem of calculus to compute
Z x
d
t sin (t) dt
dx 0
2. Compute the following definite and indefinite integrals (8 points each).
(a)
5
Z
(12x2 − 4x + 5) dx
2
(b)
18
Z
(72 − 4x) dx
0
(c)
Z
x3
dx
x4 + 1)2
Z
√
x 1 − x2 dx
Z
π/3
(d)
(e)
cos (x) dx
0
(f)
Z
cos (x)esin (x) dx
(g)
Z
1
√
√
dx
x(1 + x)3
(h)
Z
√
1
x
dx
x2 + 1
3. (10 points) Compute the area that lies between the curves y = x + 1 and y = x3 + 1.
4. (10 points) Determine the volume that is obtained by revolving the region that is
bounded by the curves y = x2 , y = 0 (the x-axis), x = 1, and x = 3 about the
x-axis.
5. (10 points) Determine the volume of the cone that is obtained by revolving the triangular region that is bounded by the lines y = 7/10x, y = 0, x = 2 and x = 10 about
the y-axis.
6. (10 points) A bag of sand, initially weighing 72 lbs, was lifted at a constant rate. As
it rose to a height of 18 feet, half of the sand leaked out at a constant rate. How much
work was done in lifting the the sand? See also Examples 2 through 5 page 378-379,
problems 1,4,5,7,8,14, and 21 page 380-381.
Rbp
7. (10 points) Use the arc-length formula L = a 1 + (y 0 )2 dx to compute the arc length
of the curve y = x3/2 from x = 0 to x = 4. See also §6.3 #1-10, page 370.
8. Problems 1-5,11,12,15-25,39-44, 51-52,55,56, and 59, §6.1 page 355-357. Problems 1-12,
23, 25,29, 31 §6.2 page 363-365.
9. §6.2 page 375, # 9,10,19,20,21.
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