CHapter 4 - AP Calculus BC CORRECT 100%

CHapter 4 - AP Calculus BC CORRECT
100%
Definite integra as the area of the region - ANSWERif f is continuous and
nonnegative on the closed interval [a,b], then the area of the region bounded by the
graph of f, the x-axis, and the vertical lines x=a and x=b is

for the fundamental theorem of calculus, it is not necessary to include a ___ in the
antiderivative - ANSWERconstant of integration C

The mean value theorem for integrals - ANSWERif f is continuous on the closed
interval [a,b], then there exists a number c in the closed interval [a,b] such that

definition of the average value of a function on an interval - ANSWERif f is integrable
on the closed interval [a,b] then the average value of f on the interval is

what is the average value of f on the interval [a,b] - ANSWERThe value of f(c) given
in the Mean Value Theorem for integrals is called the average value of f on the
interval [a,b]

Definition of one special definite integral (when integral = 0 - ANSWER1.) If f is
defined at x=a, then

2.) If f is integrable on [a,b], then

additive interval property - ANSWERif f s integrable on the three closed intervals
determined by a, b, and c, then

properties of definite integrals - ANSWERif f and g are integrable on [a,b] and k is a
constant, then the functions kf and f+-g are integrable on [a,b] and

1.)


2.)

Preservation of inequality - ANSWER1.) If f is integrable and nonnegative on the
closed interval [a,b], then...



2.) If f and g are integrable on the closed interval [a,b] and
f(x) ≤g(x) for every x in [a,b], then

Antiderentiation symbol and definte integration symbol - pg 281 - ANSWER

differentiation and definite integration have an - ANSWER"inverse" relationship