Ms Battaglia ap calculus Definite integral A definite integral is an integral with upper and lower bounds The number a is the lower limit of integration and the number b is the ID: 319947
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Slide1
4-3 definite integrals
Ms.
Battaglia
–
ap
calculus Slide2
Definite integral
A definite integral is an integral
with upper and lower bounds. The number a is the
lower limit of integration, and the number b is the upper limit of integration. Slide3
Theorem 4.4 (Continuity implies
Integrability
)
If a function f is continuous on the closed interval [a,b], then f is integrable on [a,b].Slide4
The first fundamental theorem of calculus
If f is continuous on the closed interval [
a,b
] and F is the indefinite integral of f on [a,b], thenSlide5
Evaluating a definite integralSlide6
Areas of common Geometric Figures
Sketch the region corresponding to each definite integral. Then evaluate each integral using a geometric formula.
a. b. c.Slide7
Definition of two Special integrals
If f is defined at x = a, then we define
If f is
integrable on [a,b
], then we defineSlide8
Evaluating definite integralsSlide9
Additive Interval Property
If f is
integrable
on the three closed intervals determined by a, b, and c, then Slide10
Using the Additive inverse property Slide11
Properties of Definite Integrals
If f and g are
integrable
on [a,b] and k is a constant, then the function of kf and f + g are integrable on [
a,b], and1.2.Slide12
Evaluation of a definite integral
Evaluate using each of the following values.Slide13
Preservation of Inequality
If f is
integrable
and nonnegative on the closed interval [a,b], then
If f and g are integrable on the closed interval [a,b] and f(x) < g(x) for every x in [a,b], thenSlide14
Homework
Page 278 #9
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