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Chapter 5 Integration

Chapter 5 Integration. Third big topic of calculus. Integration used to:. Find area under a curve. Integration used to:. Find area under a curve Find volume of surfaces of revolution. Integration used to:. Find area under a curve Find volume of surfaces of revolution

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Chapter 5 Integration

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  1. Chapter 5Integration Third big topic of calculus

  2. Integrationused to: • Find area under a curve

  3. Integrationused to: • Find area under a curve • Find volume of surfaces of revolution

  4. Integrationused to: • Find area under a curve • Find volume of surfaces of revolution • Find total distance traveled

  5. 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

  6. Area under a curvecan be approximatedwithout using calculus.

  7. Then we’ll do itwith calculusto find exact area.

  8. Rectangular Approximation Method5.1 • 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

  12. 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

  14. Rules for definite integrals • If f and g are integrable functions on [a,b] and [b,c] respectively • 1. 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

  16. Rules for definite integrals • If f and g are integrable functions on [a,b] and [b,c] respectively • 3. 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

  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

  19. Rules for definite integrals • If f and g are integrable functions on [a,b] and [b,c] respectively • 7. 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

  21. Rules for definite integrals • If f and g are integrable functions on [a,b] and [b,c] respectively • 9. Interval Subtraction Rule

  22. THE FUNDAMENTALTHEOREM 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. LRAM RRAM MRAM SUMMATION REIMANN SUMS RULES FOR INTEGRALS FUND. THM. CALC EVALUATE INTEGRALS FIND AREA TOTAL AREA NET AREA ETC…….. TEST 5.1-5.4

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