chapter 5 integration third big topic of calculus
TRANSCRIPT
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Chapter 5
Integration
Third big topic
of calculus
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Integrationused to:
Find area under a curve
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Integrationused to:
Find area under a curve
Find volume of surfaces of revolution
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Integrationused to:
Find area under a curve
Find volume of surfaces of revolution
Find total distance traveled
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Integrationused to:
Find area under a curve
Find volume of surfaces of revolution
Find total distance traveled
Find total change
Just to name a few
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Area under a curvecan be approximated
without using calculus.
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Then we’ll do itwith calculus
to find exact area.exact area.
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Rectangular Approximation Method5.1
Left
Right
Midpoint
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5.2 Definite Integrals
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Anatomy of an integral
integral sign
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Anatomy of an integral
integral sign
[a,b] interval of integration
a, b limits of integration
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Anatomy of an integral
integral sign
[a,b] interval of integration
a, b limits of integration
a lower limit
b upper limit
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Anatomy of an integral
integral sign
[a,b] interval of integration
a, b limits of integration
a lower limit
b upper limit
f(x) integrand
x variable of integration
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Rules for definite integrals
If f and g are integrable functions on [a,b] and [b,c] respectively
1. Zero Rule
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Rules for definite integrals
If f and g are integrable functions on [a,b] and [b,c] respectively
2. Reversing limits of integration Rule
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Rules for definite integrals
If f and g are integrable functions on [a,b] and [b,c] respectively
3. Constant Multiple Rule
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Rules for definite integrals
If f and g are integrable functions on [a,b] and [b,c] respectively
4. Sum, Difference Rule
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Rules for definite integrals
If f and g are integrable functions on [a,b] and [b,c] respectively
6. Domination Rule
6a. Special case
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Rules for definite integrals
If f and g are integrable functions on [a,b] and [b,c] respectively
7. Max-Min Rule
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Rules for definite integrals
If f and g are integrable functions on [a,b] and [b,c] respectively
8. Interval Addition Rule
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Rules for definite integrals
If f and g are integrable functions on [a,b] and [b,c] respectively
9. Interval Subtraction Rule
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THE FUNDAMENTALTHE FUNDAMENTALTHEOREM OF CALCULUSTHEOREM OF CALCULUS
PART 1 THEORY
PART 11 INTEGRAL EVALUATION
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INTEGRAL AS AREA FINDER
Area above x-axis
is positive.
Area below x-axis
is negative.
“total” area is area above – area below
“net” area is area above + area below
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TEST 5.1-5.4
LRAM
RRAM
MRAM
SUMMATION
REIMANN SUMS
RULES FOR INTEGRALS
FUND. THM. CALC
EVALUATE INTEGRALS
FIND AREA
TOTAL AREA
NET AREA
ETC……..
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