Download presentation
Presentation is loading. Please wait.
1
Chapter 5 Integration Third big topic of calculus
2
Integration used to: Find area under a curve
3
Integration used to: Find area under a curve Find volume of surfaces of revolution
4
Integration used to: Find area under a curve Find volume of surfaces of revolution Find total distance traveled
5
Integration used to: Find area under a curve Find volume of surfaces of revolution Find total distance traveled Find total change Just to name a few
6
Area under a curve can be approximated without using calculus.
7
exact area. Then we’ll do it with calculus to find exact area.
8
Rectangular Approximation Method 5.1 Left Right Midpoint
9
5.2 Definite Integrals
10
Anatomy of an integral integral sign
11
Anatomy of an integral integral sign [a,b] interval of integration a, b limits of integration
![Anatomy of an integral integral sign [a,b] interval of integration a, b limits of integration](http://images.slideplayer.com/25/7958839/slides/slide_11.jpg "Anatomy of an integral integral sign [a,b] interval of integration a, b limits of integration")
12
Anatomy of an integral integral sign [a,b] interval of integration a, b limits of integration a lower limit b upper limit
![Anatomy of an integral integral sign [a,b] interval of integration a, b limits of integration a lower limit b upper limit](http://images.slideplayer.com/25/7958839/slides/slide_12.jpg "Anatomy of an integral integral sign [a,b] interval of integration a, b limits of integration a lower limit b upper limit")
13
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
![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](http://images.slideplayer.com/25/7958839/slides/slide_13.jpg "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")
14
Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 1. Zero Rule
![Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 1.](http://images.slideplayer.com/25/7958839/slides/slide_14.jpg "Zero Rule.")
15
Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 2. Reversing limits of integration Rule
![Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 2.](http://images.slideplayer.com/25/7958839/slides/slide_15.jpg "Reversing limits of integration Rule.")
16
Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 3. Constant Multiple Rule
![Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 3.](http://images.slideplayer.com/25/7958839/slides/slide_16.jpg "Constant Multiple Rule.")
17
Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 4. Sum, Difference Rule
![Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 4.](http://images.slideplayer.com/25/7958839/slides/slide_17.jpg "Sum, Difference Rule.")
18
Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 6. Domination Rule 6a. Special case
![Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 6.](http://images.slideplayer.com/25/7958839/slides/slide_18.jpg "Domination Rule 6a. Special case.")
19
Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 7. Max-Min Rule
![Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 7.](http://images.slideplayer.com/25/7958839/slides/slide_19.jpg "Max-Min Rule.")
20
Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 8. Interval Addition Rule
![Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 8.](http://images.slideplayer.com/25/7958839/slides/slide_20.jpg "Interval Addition Rule.")
21
Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 9. Interval Subtraction Rule
![Rules for definite integrals If f and g are integrable functions on [a,b] and [b,c] respectively 9.](http://images.slideplayer.com/25/7958839/slides/slide_21.jpg "Interval Subtraction Rule.")
22
THE FUNDAMENTAL THEOREM OF CALCULUS PART 1 THEORY PART 11 INTEGRAL EVALUATION
23
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
24
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……..
Similar presentations
![Definition: the definite integral of f from a to b is provided that this limit exists. If it does exist, we say that is f integrable on [a,b] Sec 5.2:](/21/6236247/big_thumb.jpg "Definition: the definite integral of f from a to b is provided that this limit exists. If it does exist, we say that is f integrable on [a,b] Sec 5.2:>")
