## Techniques of Integration •Substitution Rule •Integration by Parts •Trigonometric Integrals •Trigonometric Substitution •Integration of Rational Functions by Partial Fractions •Rationalizing Substitutions •The Continuous Functions Which Do not Have Elementary Anti-derivatives.

Techniques of Integration

some-important-formulas-of-integration

solving-models-related-to-ordinary differential equation

differentiation-of-exponential-functions

area-between-curve

vector

application-of-derivatives

homogenous-differential-equation

inverse-trigonometry-questions

integration

integration-questions

Rolles-theorem-and-mean-value-theorem

Techniques-of-integration-substitution

critical-points-and-point-of-inflection

intermediate-value-theorem

•Substitution Rule

•Integration by Parts

•Trigonometric Integrals

•Trigonometric Substitution

•Integration of Rational
Functions by Partial Fractions

•Rationalizing Substitutions

•The Continuous Functions
Which Do not Have Elementary Anti-derivatives.

•Improper Integrals

Type I: Infinite Intervals

Type 2: Discontinuous Integrands

•Approximate Integration

Midpoint Rule

Trapezoidal Rule

Simpson’s Rule

Strategy for Integration

1. Using Table of
Integration Formulas

2. Simplify the Integrand if
Possible

Sometimes the use of algebraic manipulation or trigonometric identities
will simplify the integrand and make the method of integration obvious.

3. Look for an Obvious
Substitution

Try to find some function in the integrand whose differential also occurs,
apart from a constant factor.

3. Classify the Integrand
According to Its Form

Trigonometric functions, Rational functions,
Radicals, Integration by parts.

4. Manipulate the integrand.

Algebraic manipulations (perhaps
rationalizing the denominator or using trigonometric identities) may be useful
in transforming the integral into an easier form.

5. Relate the problem to
previous problems

When you have built up some experience in
integration, you may be able to use a method on a given integral that is
similar to a method you have already used on a previous integral. Or you may
even be able to express the given integral in terms of a previous one.

6. Use several methods

Sometimes two or three methods are required
to evaluate an integral. The evaluation could involve several successive
substitutions of different types, or it might combine integration by parts with
one or more substitutions.

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**Read more topics........**some-important-formulas-of-integration

solving-models-related-to-ordinary differential equation

differentiation-of-exponential-functions

area-between-curve

vector

application-of-derivatives

homogenous-differential-equation

inverse-trigonometry-questions

integration

integration-questions

Rolles-theorem-and-mean-value-theorem

Techniques-of-integration-substitution

critical-points-and-point-of-inflection

intermediate-value-theorem

### Applications of Integration

### Mathematics sample paper 12

### Sample paper mathematics 12

### SAMPLE QUESTION PAPER MATHEMATICS CLASS XII

### Mathematics sample paper Class XII

### Sample paper Mathematics 12

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