### Differential Equation of First order and First degree

A differential equation of first order and first degree invokes x,y andÂ So it can be put in any one …

Read More### Formation of Differential Equation

Consider a family of exponential curvesÂ where A is an arbitrary constant. For different values of A we get different …

Read More### Differential Equations

Differential Equation An equation containing an independent variable,Â dependent variable and differential coefficients of dependent variable with respect to independent …

Read More### Convergence of Improper Integral

Convergence of Improper Integral of First kind Definition 1.Â Â Â If f(x)Â is a bounded and integrableÂ function onÂ , then the improper …

Read More### Improper Integration

Improper Integrals Until now, we have beenÂ studying definite integrals of the typeÂ which were having the following features: (i) …

Read More### Integration as the limit of a sum

In this article we shall consider integration as the limit of the sum of certain number of terms when the …

Read More### Evaluation of Definite Integrals by using their properties

In this section we shall see how the properties of definite integrals are useful to evaluate definite integrals Example 1 …

Read More### Properties of Definite Integrals

In this section, we study some fundamental properties of definite integrals which are very useful in evaluating integrals Property I …

Read More### Evaluation of Definite Integrals by substitution

When the variable in a definite integral is changed, the substitution in terms of new variable should be effected at …

Read More### Definite Integrals

The Definite Integrals LetÂ be the primitive or anti-derivative of a function f(x) defined on a,b i.e.Â .Then the definite …

Read More### Integration of some special irrational algebraic functions

In this section,Â we shall discuss four integrals of the formÂ when P and Q are polynomial functions of x. …

Read More### Integration using Partial fraction

Type I When the denominator is expressible as a product of linear factors Solution: Putting x-2=0 or x=2 in (ii), …

Read More### Partial Fraction

InÂ theÂ partial fraction decompositionÂ orÂ partial fraction expansionÂ of a rational number (that is, a fractionÂ such that the numerator and the denominator are both …

Read More### Integration of various types (By Parts)

Type I : Integration of the formÂ Theorem Prove thatÂ ProofÂ Â Â We have , Algorithm Example Solution: Type II …

Read More### Integration of various types (Substitution)

Type I:Â Example Solution:Â Type II: To evaluate this type of integrals we express as the sum or difference …

Read More### Some Special Integrals

Some Special Integrals Some of the special integrals in derived form to be used where it will be applicable : …

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