MATH 101 Quiz #1 (v.A1)
Last Name:
Friday, January 15
First Name:
Grade:
Student-No:
Section:
Very short answer question
1. 1 mark Let f be a function on the whole real line. Express
Z
7
f (x) dx as a limit of Riemann
1
sums, using the right endpoints. Write your answer in the box.
Answer:
Short answer questions—you must show your work
2. 4 marks Each part is worth 2 marks.
p
R3
(a) Evaluate 3 2 + 9 x2 dx. Simplify your answer completely.
Answer:
n
X
2
e
n!1
n
i=1
(b) Express lim
i/n
cos(2i/n) as a definite integral. Write your answer in the box.
Answer:
Long answer question—you must show your work
Z
3
(x + x3 ) dx using the definition of the definite integral. You may use the
0
P
P
2
4
3
2
summation formulas ni=1 i = n 2+n and ni=1 i3 = n +2n4 +n . You may leave your answer in
“calculator-ready” form. (No credit will be given for using integration rules, but you may use
them to check your answer.)
3. 5 marks Find