chapter 7- integration - corporate rishi€¦ · indefinite and definite integrals, including the...

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 BY INSPECTION, SUBSTITUTION & PARTS

Integration by inspection

Integration using partial fractions


Integration by substitution (change of variable)


Integration by parts


Differentiating an integral (Leibniz’s formula)


CONVERGENCE

DOUBLE INTEGRALS

Swapping the order of integration

DOUBLE INTEGRALS

DOUBLE INTEGRALS

NUMERICAL METHODS FOR INTEGRATION

The trapezium rule

THE TRAPEZIUM RULE

TAYLOR & MACLAURIN SERIES

Taylor series

TAYLOR AND MACLAURIN SERIES


Maclaurin series

DIFFERENTIAL EQUATIONS

Solution by direct integration


Solution by separation of variables


Solution by integrating factor

chapter 7- integration - corporate rishi€¦ · indefinite and definite integrals, including the...

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