Problem 1
The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of
30 seconds is shown. Estimate the distance traveled during this period
0
10
20
30
0
40
80
120
t (seconds)
1
v
(km/h)Problem 2
Using Definition 2, find an expression for the area under the function f(x) = x
2
e
x on the
interval 0 ≤ x ≤ 4. Do not evaluate the limit.
2 Definition The area A of the region S that lies under the graph of the
continuous function f is the limit of the sum of the areas of approximating
rectangles:
A = lim
n→∞
Rn = lim
n→∞
[f(x1)∆x + f(x2)∆x + · · · + f(xn)∆x]
Problem 3
Determine a region whose area is given by limn→∞ P
n
i=1 n
1