MATH 210 OCC Integrals Questions

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Truman City College
Department of Mathematics
Math 210
Math Center Review
Fall 2022
Please complete the following problems. Make sure that a CCC Math Center staff person has reviewed
your solutions and determined that all solutions are correct. You will need to upload your solutions to
Brightspace including the signature of a Math Center staff person. The due date is EOD Friday, 23
September.
1. Evaluate the following integrals.
(a)
Z
x ln x dx
(b)
Z
1
dx
x2 ? 9
(c)
Z
?
cos x
?
x
(d)
Z
1
x2 + 4x + 5
dx
(e)
Z
1
x2 + 4x ? 5
(f)
dx
Z
ex
?
dx
1 ? ex
Z
x
?
dx
1 + x2
Z
1
?
dx
1 + x2
(g)
(h)
(i)
Z
(j)
sin4 x cos3 x dx
Z ?
0
1
sin2 2x dx
(k)
Z e
x ln x dx
1
(l)
Z 1
0
(m)
Z ?
0
1
?
dx
3
x
1
?
dx
3
x
(n)
x2 + x + 1
dx
x3 + x
Z
(o)
Z
ln (ln x)
dx
x ln x
2. Compute the Taylor polynomial of order seven about x = 0 generated by the function f (x) =
x ln (1 + x).
3. Use the polynomial in question 2 to compute f (7) (0).
4. Find the first three terms of the Maclaurin Series for
x
f (x) = ?
dx
1+x
5. Find the first five terms of the power series representation for tan?1 x2 .
6. Find the values of p for which the series below is convergent.
?
X
1
n(ln n)p
n=2
7. A ball is dropped from 100 feet. Every time it hits the ground, it rebounds to 1/3 of its previous
height. Find the total distance the ball travels.
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