If you mean the the integral of sin(x2)dx, It can only be represented as an infinite series or a unique set of calculus functions known as the Fresnel Integrals (Pronounced Frenel). These functions, S(x) and C(x) are the integrals of sin(x2) ans cos(x2) respectively. These two integrals have some interesting properties. To find out more, go to:
http://en.wikipedia.org/wiki/Fresnel_integral
I hope this answers your question.
8
Do you mean the Convolution Integral?
The integral of -x2 is -1/3 x3 .
2 2x makes no sense. If you meant the integral of 2x, it is x2 + C. If you meant the integral of 4x, it is 2x2 + C. If you meant the integral of 2x2, it is 2/3 x3 + C.
The Lebesgue integral covers a wider variety of cases. Specifically, the definition of hte Riemann integral permits a finite number of discontinuities; the Lebesgue integral permits a countable infinity of discontinuities.
The integral of sin x2 is one of the Fresnel Integrals. It does not have a closed form solution. However, you can calculate a series solution by integrating the Taylor series, as follows: The Taylor series expansion about x = 0 for sin x is sin x = x - (x3/3!) + (x5/5!) - (x7/7!) +/- ... Substitution of x2 for x yields sinx2 = x2 - (x6/3!) + (x10/5!) - (x14/7!) +/- ... Term-wise integration, using the power rule gives {integral}sinx2 = (x3/3) - (x7/7*3!) + (x11/11*5!) - (x15/15*7!) +/- ... This is the answer. It is the Fresnel Integral S(x). There is a similar one for the integral of cos x2, called C(x). It can be written in more compact form: S(x) = (Sum from n = 1 to infinity) of (-1)n x4n+3/(4n+3)*(2n+1)! It looks better in Sigma notation, with fractions, but if you work out the first 4 terms, you will see agreement with the result for integrating the series expansion. Here is a link to Fresnel Integral on Wikipedia: http://en.wikipedia.org/wiki/Fresnel_integral Thank you for posing this question.
8
Integral in Tagalog: mahalaga
In reimann stieltjes integral if we assume a(x) = x then it becomes reimann integral so we can say R-S integral is generalized form of reimann integral.
What is a integral
Do you mean the Convolution Integral?
Elections are integral to democracies.
non integral is type of numbers behaviour: i can say that set of numbers without any "holes inside" are integral and set of numbers with "holes inside are non integral. example : integral group "1..100" non integral group "1,4,8,67"
Political parties are an integral part of democracy. Religion is an integral part of Saudi Arabia. Greed is an integral part of human psychology.
Particular integral is finding what the integral is for example the integral of 2x is x^2 + C. Finding the particular solution would be finding what C equals from the particular integral.
First we have to evaluate the inner integral using ILATE method and then evaluate the outer integral
Integral Systems was created in 1982.