Definite Integral Review

Question 1

How well do you feel you are understanding the Fundamental Theorem of Calculus?

Accepted Answer

Pretty well., What's that?, This is child's play!, I'm getting there.

Question 2

How important is the Fundamental Theorem of Calculus?

Accepted Answer

I better know it or else!

Question 3

True or False. Integrating v(t) over a time interval always gives the distance traveled.

Accepted Answer

False

Question 4

When you know velocity and you want position, what should you do?

Accepted Answer

Set up a definite integral of velocity

Question 5

True or False. ∫ [f(x) + g(x)] dx = ∫ f(x)dx + ∫ g(x)dx

Accepted Answer

True

Question 6

What is the hypothesis of the Mean Value Theorem for Derivatives?

Accepted Answer

f is continuous on [ a , b ] and differentiable on ( a , b )

Question 7

What is the conclusion to the Mean Value Theorem for Derivatives?

Accepted Answer

f'(c) = [f(b)-f(a)] / (b-a)

Question 8

True or False. When using integrals to find area, it's OK to get a negative area.

Accepted Answer

False

Question 9

True or False. If f(x) is continuous on [ a , b ] , then f is integrable on [ a , b ].

Accepted Answer

True

Question 10

How many parts are in the Fundamental Theorem of Calculus?

Accepted Answer

2 but 1 of the parts has two parts, weird

Question 11

What is the area under one arch of a cosine curve?

Accepted Answer

2

Question 12

Distance traveled is sometimes, always, or never the same as displacement.

Accepted Answer

Sometimes

Question 13

True or False. Integrating |v(t)| over a time interval always gives the distance traveled.

Accepted Answer

True

Question 14

True or False. The value of ∫ab f(x)dx must be positive.

Accepted Answer

False

Question 15

True or False. LRAM is too high when f(x) is decreasing.

Accepted Answer

True

Questions 15