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MATH 122 EXAM 1
JANUARY 28, 2011
NAME: SECTION:
ONLY THE CORRECT ANSWER AND ALL WORK USED TO REACH IT WILL
EARN FULL CREDIT.
Simplify all answers as much as possible unless explicitly stated otherwise.
This is a closed-book, closed-notes exam. No electronic devices are allowed.
IF YOUR SECTION NUMBER IS MISSING OR INCORRECT, 5 POINTS WILL BE DEDUCTED FROM YOUR SCORE.
Points PAGE 2 PAGE 3 PAGE 4 PAGE 5 PAGE 6 PAGE 7 28 points 28 points 14 points 14 points 8 points 8 points Score
Total Score:
FORMULAS
∑^ n
k=
1 = n
∑^ n
k=
k =
n(n + 1) 2
∑^ n
k=
k^2 =
n(n + 1)(2n + 1) 6
∑^ n
k=
k^3 =
[
n(n + 1) 2
] 2
1
2 JANUARY 28, 2011
Evaluate the following indefinite integrals by any method. (7 points each.)
5 x^1 /^4 + (^) x 31 / 4
dx
∫ (^) t 3 − 5 t^2 dt
∫ sec^2 (
√y
√y dy
∫ (^) ex √ 1 −e^2 x^ dx
4 JANUARY 28, 2011
(9) (7 points.) Write the sum 1 − 3 + 5 − 7 + 9 − 11 in sigma notation.
(10) (7 points.) Approximate the area between the graph of y = sin x and the x-axis over the interval [0, π], dividing the interval into n = 3 subintervals, and choosing x∗ k to be the right endpoint of each subinterval.
MATH 122 EXAM 1 5
(11) (8 points.) Let f (x) be differentiable, let
1 f^ (x)dx^ = 4, and let^
1 f^ (x)dx^ = 7. Evaluate the following.
(a)
f ′(x)dx
(b)
2 f^ (x)dx
(c)
5 f^ (x)dx
(12) (6 points.) Let F (x) =
∫ (^) x 2 ln(t)dt. Evaluate the following.
(a) F (2)
(b) F ′(2)
(c) F ′′(2)
6 JANUARY 28, 2011
(13) (8 points.) Evaluate the definite integral
− 2 (3 +^ |x|)^ dx^ by^ any method.
MATH 122 EXAM 1 7
(14) (a) (4 points.) Write the exact area between the graph of y = x(2 − x) and the x-axis over the interval [0, 1] as the limit of a Riemann sum with x∗ k as the right endpoint of each subinterval. Make all of your subintervals of equal length. You need not evaluate the limit. You do not need to put the sum in closed form.
(b) (4 points.) Find the exact area between the graph of y = x(2 − x) and the x-axis over the interval [0, 1], by any method.
