Math 113, Calculus II
Test 2: Review
1
1.1
Integration
Improper Integrals
Improper integrals arise when an infinity or an undefined point appears either in the integrand, the interval, or the integral
Math 113, Calculus II
Winter 2007
Final Exam - Solutions
1. (25 points) Use the limit definition of the definite integral and the sum formulas1 to compute
3 1
3x2 - 4x + 1 dx.
Then check your answer u
Math 113, Calculus II
Test 2 - Solutions
1. (25 points) Consider the region bounded by the curves y = x2 and y = 2x - x2 . (a) Sketch the curves and shade in the region bounded by them. 2
y = x2
1 y =
Math 113, Calculus II
Final Exam Solutions
1
1. (25 points) Use the limit definition of the definite integral and the sum formulas
2 -2
to compute
4 - x2 dx.
Then check your answer using the Evaluatio
Math 113, Calculus II 1. (25 points) Consider the region bounded by the curves x 2 = y 3 and y = 1. (a) Sketch both curves and shade in the region. 2
Test 2 Solutions
x2 = y 3
1
y=1
-2
-1 -1
1
2
(b) F
Test 1 - Solutions
Math 113, Calculus II
February 2, 2007
1. (30 points) Use the limit definition of the definite integral and the sum formulas1 to compute
1 -1
3x2 - 4x + 7 dx.
Then check your answer
Calculus II Final Exam Problems - Solutions
1
1. Use the definition of the definite integral to evaluate1
1 -1
(3x - x2 ) dx.
Solution: Recall the limit definition of the definite integral:
b n
f (x)
Math 113, Calculus II
Solutions for Test 2: Review
1
Practice Problems - Solutions
1. Determine whether the following series are convergent or divergent. Specify the test you use in each part! (a) n2
Math 113, Calculus II
Test 1: Review Solutions
1. Use the limit definition of the definite integral to evaluate
5
(4x - x2 )dx.
2
Solution: By definition, 2 (4x - x2 )dx = limn n f (x )x, where x = b-
Math 113, Calculus II
Test 1: Review
1
Review of the material
Chapter 5 is an introduction to integral calculus. In this chapter we study techniques for evaluating both definite and indefinite integra
GE GCX b6s GX 4 GX d X X s v wr X W v u W Wr F P H Q VW [email protected] A` p @ F D q o Q pW P H F P H VW Q V q U`e4e4G$A H q P H D F D q o Y q H H D p T F P H VW F u D D $GiGAi8e$GX4GGq w 06` 06z o Q V $
Math 113, Calculus II
Test 1 Solutions
1. (25 points) Use the limit definition of the definite integral and the sum formulas to compute
0
x2 +
-3
4 3
dx.
Then check your answer using the Evaluation Th