True/False Quizzes for
Applied Calculus
Topic: The Integral
(Chapter 6)

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1. If F(x) is an antiderivative of f(x), then f'(x) = F(x).
2. If c(x) is the marginal cost function, then the cost function is c(x) dx.
3. When you've seen one antiderivative of f(x), you've seen them all.
4. The integral of a sum is the sum of the integrals.
5. The integral of a difference is the difference of the integrals.
6. The integral of a product is the product of the integrals.
7. The integral of a quotient is the quotient of the integrals.
8.
2

0
ex dx = e2
9.
ex2 dx=
ex2

2x
+ C
10.
ln x=
1

x
11.
ln x dx=
1

x
+ C
12.
b

a
f(x) dx=F(b) - F(a),where F is an antiderivative of f.
13.
b

a
f(x) dx is the area enclosed by the graph of f, the x-axis, and the vertical lines x = a and x = b.
14.
If s(t) represents total sales after t months, then total sales from month a to month b are given byb

a
s(t) dt.
15. The left-hand Riemann sum of a continuous function f(x) is always its right-hand Riemann sum.
16. The trapezoidal Riemann sum of a continuous function f(x) is always midway between its left-hand and right-hand sums.
17.
1

4x2+x
dx=ln |4x2+x| + C
18. The function f(x) = ex2 has an antiderivative involving functions with which we are familiar.
19. The function f(x) = ex2 has no antiderivative.
20. If you throw a ball upwards with twice the velocity that I do, then yours will rise twice as far as mine.

Last Updated: August, 1999
Copyright © 1999 Stefan Waner & Steven R. Costenoble