What is the integral of sin(t^2)?

Question

What is the integral of sin(t^2)?

well i have to find the integral of xsin(x^2) from 0 to 10, and im trying by parts but have no luck in doing so.

Answer 1

There is no expression for this integral in terms of common functions. Mathematics often encounter integrals like this and have to make up new functions. In cases like these they use functions called Fresnel Integrals.

∫sint²dt = √[π/2] FresnelS( √[2/π] t )

Answer 2

Integral Of Sin T 2

Answer 3

The integral of sin(x²) is called a Fresnel integral.It
can't be expressed in terms of elementary functions.
So let's do your integral another way.
∫ x sin x² dx.
Let u = x² dx = 2x dx. Then we get
½ ∫sin u du = -½ cos u = -½ cos(x²) + C.
Evaluating this from 0 to 10 the final result is
-½[ cos(100) - 1].

Answer 4

Integral of sin(t^2)d(t^2) = - cos(t^2) + C
(I can't type that elongated S shape for integration, so I just said
"Integral of")

teddy boy

Answer 5

∫sin(t^2) dt

sin(t) can be expressed as infinite series

sin(t) = t - t^3/3! + t^5/5! - t^7/7! ----------------


now replace t with t^2

sin(t^2) = t^2 - t^6/3! + t^10/5! ---------------------

∫sin(t^2) dt = ∫t^2 dt - 1/6∫t^6 dt + 1/120∫t^10 dt -----------------

=> t^3/3 - (1/42)t^7 + (1/1320)t^11 ------------------

you can continue like this depending upon the accuracy you want