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  e^{x} dx = e^{2} 

9. 


 e^{x2} dx  =  e^{x2}
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 xaxis, 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   b
a  s(t) dt. 

15. 


The lefthand Riemann sum of a continuous function f(x) is always its righthand Riemann sum. 
16. 


The trapezoidal Riemann sum of a continuous function f(x) is always midway between its lefthand and righthand sums. 
17. 


 1
4x^{2}+x  dx  =  ln 4x^{2}+x + C 

18. 


The function f(x) = e^{x2} has an antiderivative involving functions with which we are familiar. 
19. 


The function f(x) = e^{x2} 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. 