0
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.
Add your answer:
Earn +20 pts
Integral of sine squared x?
.5(x-sin(x)cos(x))+c
Integral of 1 divided by sinx cosx?
Integral of [1/(sin x cos x) dx] (substitute sin2 x + cos2 x for 1)= Integral of [(sin2 x + cos2 x)/(sin x cos x) dx]= Integral of [sin2 x/(sin x cos x) dx] + Integral of [cos2 x/(sin x cos x) dx]= Integral of (sin x/cos x dx) + Integral of (cos x/sin x dx)= Integral of tan x dx + Integral of cot x dx= ln |sec x| + ln |sin x| + C
What is the integral of cosec squared x?
-cotan(x)
What is Sin squared x - Cos squared x divided by 1 - Tan squared x equals cos squared x?
22
What does 1 - cos squared equal?
Note that an angle should always be specified - for example, 1 - cos square x. Due to the Pythagorean formula, this can be simplified as sin square x. Note that sin square x is a shortcut of (sin x) squared.
Integral of sine squared x?
.5(x-sin(x)cos(x))+c
Integral of 1 divided by sinx cosx?
Integral of [1/(sin x cos x) dx] (substitute sin2 x + cos2 x for 1)= Integral of [(sin2 x + cos2 x)/(sin x cos x) dx]= Integral of [sin2 x/(sin x cos x) dx] + Integral of [cos2 x/(sin x cos x) dx]= Integral of (sin x/cos x dx) + Integral of (cos x/sin x dx)= Integral of tan x dx + Integral of cot x dx= ln |sec x| + ln |sin x| + C
Why sin integral is cos?
sin integral is -cos This is so because the derivative of cos x = -sin x
What is sine squared?
Answer 1 Put simply, sine squared is sinX x sinX. However, sine is a function, so the real question must be 'what is sinx squared' or 'what is sin squared x': 'Sin(x) squared' would be sin(x^2), i.e. the 'x' is squared before performing the function sin. 'Sin squared x' would be sin^2(x) i.e. sin squared times sin squared: sin(x) x sin(x). This can also be written as (sinx)^2 but means exactly the same. Answer 2 Sine squared is sin^2(x). If the power was placed like this sin(x)^2, then the X is what is being squared. If it's sin^2(x) it's telling you they want sin(x) times sin(x).
What is sin squared x minus cos squared x?
Sin squared, cos squared...you removed the x in the equation.
What is the integral of the sine of x divided by the cosine squared of x with respect to x?
∫ sin(x)/cos2(x) dx = sec(x) + C C is the constant of integration.
What is the integral of cosec squared x?
-cotan(x)
Integral of sec squared radical x?
integral of radical sinx
What is the integral of sin x?
-cos x + Constant
Is 2 sin squared x the same as 2 sin x?
No.
Integral of x cosx dx?
The integral of x cos(x) dx is cos(x) + x sin(x) + C
Cos x sin x integral?
sin2x + c
