Calculus 2 Chapter 5.4 - 5.5

Question 1

What is the indefinite integral?

Answer 1

Check example 4 in chapter 5.4

Question 2

What is the difference between definite integral and indefinite integral?

Answer 2

Check example 5 in chapter 5.4

Question 3

What are the 15 must knows in chapter 5.4?

Answer 3

Check example 6 in chapter 5.4

Question 4

What is the Net Change Theorem?

Answer 4

Check Net Change Theorem (example 8) in chapter 5.4

Question 5

What is the substitution rule for indefinite integral and what is it the substitution rule for Definite Integral

Answer 5

Check example 4 and 7 in chapter 5.5

Question 6

What are the three Pythagorean identities?

Answer 6

sin^2 (t) + cos^2 (t) = 1

tan^2 (t) + 1 = sec^2 (t)

1 + cot^2 (t) = csc^2 (t)

Question 7

What are six Angle-Sum and -Difference Identities?

Answer 7

sin(α + β) = sin(α) cos(β) + cos(α) sin(β)
sin(α – β) = sin(α) cos(β) – cos(α) sin(β)
cos(α + β) = cos(α) cos(β) – sin(α) sin(β)
cos(α – β) = cos(α) cos(β) + sin(α) sin(β)
tan(α+β) = [tan(α)+tan(β)] / [1-tan(α)tan(β)]
tan(α−β) = [tan(α)−tan(β)] / [1+tan(α)tan(β)]

Question 8

What are three double-angle identities?

Answer 8

sin(2x) = 2 sin(x) cos(x)

cos(2x) = cos^2 (x) – sin^ 2(x) = 1 – 2 sin^ 2 (x) =
2 cos^2 (x) – 1

tan(2x) = [2tan(x)] / [1−tan^2 (x)]

Question 9

Even or odd?

Answer 9

Check example 9 in chapter 5.5