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Chapter 7- Integration
● Indefinite and definite integrals, including the area under a graph● Integrating standard functions● Integrating by inspection, by substitution, and by parts● Convergence of definite integrals● Multiple integrals● Numerical methods for integration● Taylor series and Maclaurin series● Simple ordinary differential equations.
INTEGRALS
Integration and differentiation are connected in that they are the “reverse” of each other.
Integrals with limits are called definite integrals.
INTEGRALS
INTEGRATION OF STANDARD FUNCTIONS
INTEGRATION OF STANDARD FUNCTIONS
INTEGRATION OF STANDARD FUNCTIONS
INTEGRATION OF STANDARD FUNCTIONS
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
Integration by inspection
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
Integration using partial fractions
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
Integration by substitution (change of variable)
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
Integration by parts
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
Differentiating an integral (Leibniz’s formula)
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
INTEGRATION BY INSPECTION, SUBSTITUTION & PARTS
CONVERGENCE
CONVERGENCE
CONVERGENCE
CONVERGENCE
DOUBLE INTEGRALS
DOUBLE INTEGRALS
DOUBLE INTEGRALS
DOUBLE INTEGRALS
DOUBLE INTEGRALS
DOUBLE INTEGRALS
Swapping the order of integration
DOUBLE INTEGRALS
DOUBLE INTEGRALS
NUMERICAL METHODS FOR INTEGRATION
The trapezium rule
THE TRAPEZIUM RULE
THE TRAPEZIUM RULE
TAYLOR & MACLAURIN SERIES
Taylor series
TAYLOR AND MACLAURIN SERIES
TAYLOR AND MACLAURIN SERIES
TAYLOR AND MACLAURIN SERIES
TAYLOR AND MACLAURIN SERIES
TAYLOR AND MACLAURIN SERIES
TAYLOR AND MACLAURIN SERIES
TAYLOR AND MACLAURIN SERIES
Maclaurin series
TAYLOR AND MACLAURIN SERIES
TAYLOR AND MACLAURIN SERIES
DIFFERENTIAL EQUATIONS
Solution by direct integration
DIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONS
Solution by separation of variables
DIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONS
Solution by integrating factor
DIFFERENTIAL EQUATIONS