Download Sample 3 - Trimble County Schools

AP Calculus
Quiz 4.1-4.5
Name_________________________
Evaluate the following integrals:
1.
 6dx
2.  (3x 2  2 x  5)dx
3.

4.
5
x 2 dx
 3 sec
2
xdx
5. Find f (x) if f ( x)  x  2 , f (0)  3 , and f (0)  1 .
6. a) What is a definite integral used to find?
b) State one difference between an indefinite integral and a definite integral.
7. Use the properties of sigma notation and the summation formulas evaluate the given
10
sum:
i
2
 2i  3
7
f ( x)dx  8 and
i 1
8. Given

0

7
1
f ( x)dx  3 , find
1

0
f ( x)dx .
9.State the Fundamental Theorem of Calculus using math symbols.
10. Use the Fundamental Theorem of Calculus to evaluate

2
1
1
dx . Show all work.
x2
11. Evaluate:
d x
(2t 2  5) 2 dt

1
dx
12. Using a u-substitution, evaluate the following integral:
x
8  4 x 2 dx
Bonus: Use a(t )  32 ft / s 2 as the acceleration due to gravity. A ball is thrown
vertically upward from the ground with an initial velocity of 56 ft / s . For how many
seconds will the ball be going upward?