11012 MATH Name:
Intuitive Calculus
KSU .
Integration Homework
1. Consider the function f whose graph is given.
y 2 1
-3
-2
-1
O -1 -2
1
2
3
4
5
6
7
t
Evaluate each of the following integrals using the graph of f .
0 3 5
(a)
-3 1
f (x) dx
(c)
0 6
f (x) dx
(e)
1
f (x) dx
(b)
-1
f (x) dx
(d)
3
f (x) dx
7
(f)
-2
f (x) dx
2. Consider the function f whose graph is given.
y 2 1
-3
-2
-1
O -1 -2
1
2
3
4
5
6
7
t
Evaluate each of the following integrals using the graph of f .
-2 3 7
(a)
-3 0
f (x) dx
(c)
-1 6
f (x) dx
(e)
6
f (x) dx
(b)
-3
f (x) dx
(d)
3
f (x) dx
7
(f)
-3
f (x) dx
3. Suppose the following is the graph of a widget manufacturer's marginal cost function, M C(x), (in dollars per widget) as a function of the number, x, of widgets produced.
4 3
2
O
100
300
500
700
Write each of the following in terms of an integral. Then evaluate using the graph of M C. Include units in your answer. (a) What is the total cost of producing the first 200 widgets?
(b) What is the total cost of producing the first 300 widgets?
(c) What is the total cost of producing the first 500 widgets?
(d) What is the total cost of producing the first 600 widgets?
(e) What is the total cost of producing 50th the through 100th widgets?
(f) What is the total cost of producing the 350th through 400th widgets?
(g) What is the total cost of producing the 550th through 600th widgets?
(h) What is the total cost of producing the 400th through 700th widgets?
4. Suppose the following is the graph of a moving object's velocity v, in feet per second, as a function of time t, in seconds.
y 2 1
-3
-2
-1
O -1 -2
1
2
3
4
5
6
7
t
Write each of the following in terms of an integral. Then evaluate using the graph of v. Include units in your answer. (a) What is the displacement of the object from t = -2 to t = 1?
(b) What is the total distance traveled by the object (without regard to direction) from t = -2 to t = 1?
(c) What is th...