what is the antiderivative of f(x)=2sin(x^2)?
2006-09-23 17:58:43 · 7 answers · asked by fender_tri 1 in Science & Mathematics ➔ Mathematics
=sqrt(2pi))S{x*sqrt(2/pi)},
where S is the Fresnel integral
2006-09-23 18:32:19 · answer #1 · answered by Helmut 7 · 0⤊ 0⤋
You can't get an indefinite integral for this, but you have some choices, first of all express sin (x^2) as an infinite series (i.e use a Taylor expansion) and integrate term by term.
You can make use of a polar integral like the case of ∫ e^(-x^2) dx
to get the integral from -infinity to infinity or 0 to infinity.
If of course f'(x) = 2x sin (x^2)
let t = x^2
dt/dx = 2x
then it becomes ∫ sin t dt = -cos t +c = -cos (x^2) + c
where c is an arbitrary constant of integration.
2006-09-23 21:57:18 · answer #2 · answered by yasiru89 6 · 0⤊ 0⤋
lol, i hope you know that antiderivatives also means integrals, if that helps any. it's been too long since i took calculus.
actually, i think it would be -4cos(x). the integral/antiderivative of sin(x) is -cos(x). take the chain rule of x^2, which gives you 2x. since there's a coefficient of 2, you would multiply the 2x with the 2 to get the 4x, giving you the answer of -4xcos(x). and again, i'm not sure because of my old memory in calculus.
2006-09-23 18:02:30 · answer #3 · answered by dharken2 2 · 0⤊ 0⤋
Are you sure it wasn't the antiderivative of f(x) = 2x sin (x^2) ?
2006-09-23 18:14:10 · answer #4 · answered by z_o_r_r_o 6 · 0⤊ 0⤋
Mathematics can be impressive, but when I had to do calculus at 8:00am every day of the week, it sapped my will to live!!!
2006-09-23 18:04:37 · answer #5 · answered by Jeremy D 5 · 0⤊ 0⤋
∫2 sinx² =
- (cos x²) / x
2006-09-23 18:54:30 · answer #6 · answered by M. Abuhelwa 5 · 0⤊ 1⤋
-cos(x^2)
2006-09-23 18:03:06 · answer #7 · answered by wild_turkey_willie 5 · 0⤊ 1⤋