280 likes | 399 Views
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
E N D
Chapter 5Integration Third big topic of calculus
Integrationused to: • Find area under a curve
Integrationused to: • Find area under a curve • Find volume of surfaces of revolution
Integrationused to: • Find area under a curve • Find volume of surfaces of revolution • Find total distance traveled
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
Area under a curvecan be approximatedwithout using calculus.
Rectangular Approximation Method5.1 • Left • Right • Midpoint
Anatomy of an integral • integral sign
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 • 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 • f(x) integrand • x variable of integration
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 • 2. Reversing limits of integration Rule
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 • 4. Sum, Difference Rule
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 • 7. Max-Min Rule
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 • 9. Interval Subtraction Rule
THE FUNDAMENTALTHEOREM OF CALCULUS • PART 1 THEORY • PART 11 INTEGRAL EVALUATION
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
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