A. Definite integral can be used to calculate percentage rate of change of the function b. Lorenz curves are special curves used to capture demand elasticity
c. Integration by parts formula is the fundamental formula used to conduct marginal analysis
d. Definite integral can be used to calculate area under a curve in a given interval

d. Definite integral can be used to calculate area under a curve in a given interval

General Formulas and Concepts:

Calculus

Integration

Area of a Region Formula:                                                                                    

Step-by-step explanation:

We know that by definition, an integral is an antiderivative.

Also by definition, an integral is also the area under the curve. This can be extended to area between 2 curves.

We have a formula specifically to find an area under a curve (region), as listed above.

∴ our answer is D.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560