if you can solve it , i would be appreciated

Problem 1 30 pts]: Many integrals that arise in applications can terms of functions from calculus (like exponentials, trigonometric functions, logarit etc) that we have studied. One important type of such integrals are called Fresnel integrals, which e study of optics. There are two sill integrals: S() :=/ sin( ) at and A. 6 pts Use the Taylor series for cos(t) and the rules discussed in class to show that the Taylor series for cos(t ) at centered at 2- is In order to earn full credit, show your work in summation notation and perform all calculations