BC Definite Integral Review

Question 1

Integrating |v(t)| over a time interval always gives ....

Accepted Answer

Distance Travelled

Question 2

A definite integral, if it exists, is sometimes, always, or never a real number.

Accepted Answer

Always

Question 3

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

Accepted Answer

True

Question 4

What is the area under f(x)= 1/x2 from x = 1 to x = 2?

Accepted Answer

1/2

Question 5

How important is the Fundamental Theorem of Calculus?

Accepted Answer

I better know it or else!

Question 6

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

Accepted Answer

False

Question 7

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 8

Find the total area of the region between cos(x) and the x-axis on 0 ≤ x ≤ π/2

Accepted Answer

1

Question 9

Find the total area of the region between the curve and the x-axis. y = 3x 2 - 3, - 2 ≤ x ≤ 2

Accepted Answer

12

Question 10

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

Accepted Answer

True

Question 11

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

Accepted Answer

True

Question 12

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

Accepted Answer

Sometimes

Question 13

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

Accepted Answer

2

Question 14

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

Accepted Answer

False

Question 15

Integrating v(t) over a time interval gives...

Accepted Answer

Change in Position

Question 16

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

Accepted Answer

Set up a definite integral with velocity as the integrand.

Questions 16