Sunday, May 9, 2010

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integration's formula

Composed functions:

  • \int \cos ax\, e^{bx}\, dx = \frac{e^{bx}}{a^2+b^2}\left( a\sin ax + b\cos ax \right) + C
  • \int \sin ax\, e^{bx}\, dx = \frac{e^{bx}}{a^2+b^2}\left( b\sin ax - a\cos ax \right) + C
  • \int \cos ax\, \cosh bx\, dx = \frac{1}{a^2+b^2}\left( a\sin ax\, \cosh bx+ b\cos ax\, \sinh bx \right) + C
  • \int \sin ax\, \cosh bx\, dx = \frac{1}{a^2+b^2}\left( b\sin ax\, \sinh bx- a\cos ax\, \cosh bx \right) + C


Absolute value functions:
  • \int \left \sin{ax} \right\,dx = {-1 \over a} \left \sin{ax} \right \cot{ax} + C
  • \int \left (ax + b)^n \right\,dx = {(ax + b)^{n+2} \over a(n+1) \left ax + b \right} + C \,\, [\,n\text{ is odd, and } n \neq -1\,]
  • \int \left \cos{ax} \right\,dx = {1 \over a} \left \cos{ax} \right \tan{ax} + C
  • \int \left \tan{ax} \right\,dx = {\tan(ax)[-\ln\left\cos{ax}\right] \over a \left \tan{ax} \right} + C
  • \int \left \csc{ax} \right\,dx = {-\ln \left \csc{ax} + \cot{ax} \right\sin{ax} \over a \left \sin{ax} \right} + C
  • \int \left \sec{ax} \right\,dx = {\ln \left \sec{ax} + \tan{ax} \right \cos{ax} \over a \left \cos{ax} \right} + C
  • \int \left \cot{ax} \right\,dx = {\tan(ax)[\ln\left\sin{ax}\right] \over a \left \tan{ax} \right} + C
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integration's formula

Trigonometric functions


\int \sin{x}\, dx = -\cos{x} + C
\int \cos{x}\, dx = \sin{x} + C
\int \tan{x} \, dx = -\ln{\left| \cos {x} \right|} + C = \ln{\left| \sec{x} \right|} + C
\int \cot{x} \, dx = \ln{\left| \sin{x} \right|} + C
\int \sec{x} \, dx = \ln{\left| \sec{x} + \tan{x}\right|} + C
\int \csc{x} \, dx = \ln{\left| \csc{x} - \cot{x}\right|} + C
\int \sec^2 x \, dx = \tan x + C
\int \csc^2 x \, dx = -\cot x + C
\int \sec{x} \, \tan{x} \, dx = \sec{x} + C
\int \csc{x} \, \cot{x} \, dx = -\csc{x} + C
\int \sin^2 x \, dx = \frac{1}{2}\left(x - \frac{\sin 2x}{2} \right) + C = \frac{1}{2}(x - \sin x\cos x ) + C
\int \cos^2 x \, dx = \frac{1}{2}\left(x + \frac{\sin 2x}{2} \right) + C = \frac{1}{2}(x + \sin x\cos x ) + C
\int \sec^3 x \, dx = \frac{1}{2}\sec x \tan x + \frac{1}{2}\ln|\sec x + \tan x| + C
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shayri

G :- ગજબ
U :- યાદ રહીજાય તેવા
J :- જક્કાસ
A :- અલ્ટિમેટ
R :- રાપ્ચિક
A :- એડવાન્સ
T :- ટકાટક
I :- ઈન્ટેલીજન્ટ

હવે ગુજરાતીમાં

ગુ :- ગુચવી નાખે તેવા
જ :- જબ્બર માઈન્ડ વાળા
રા :- રાજ કરે એવા(બધાના દિલો પર)
તી :- તીર જેવા ધારદાર.

આને કહેવાય original ગુજરાતી
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sachin's 200*

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basic formula

Basic formula:



Additive Inverse

a + (-a) = 0

Associative of Addition

(a + b) + c = a + (b + c)

Commutative of Addition

a + b = b + a

Definition of Subtraction

a - b = a + (-b)

Closure Property of Multiplication

Product (or quotient if denominator (!=)0) of 2 reals equals a real number

Multiplicative Identity

a * 1 = a

Multiplicative Inverse

a * (1/a) = 1 (a (!=) 0)

(Multiplication times 0)

a * 0 = 0

Associative of Multiplication

(a * b) * c = a * (b * c)

Commutative of Multiplication

a * b = b * a

Distributive Law

a(b + c) = ab + ac

Definition of Division

a / b = a(1/b)
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Saturday, May 8, 2010

commedy circus

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i love india

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wwe-john vs khali

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raas-garba

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jo chlne lage-jab we met

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