## 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.
 20 ex dx = e2
9.
 ex2 dx = ex22x + C
10.
 ln x = 1x
11.
 ln x dx = 1x + C
12.
 ba f(x) dx = F(b) - F(a), where F is an antiderivative of f.
13.
 ba 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 by ba 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.
 14x2+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