Print your name(s).nn here: Problem 1 [35 pts]: Many integrals that arise in applications cannot be evaluated in terms of the common functions from calculus (like exponentials, trigonometric functions, logarithms, polynomials, etc) that we have studied. One important type of such integrals are called Fresnel integrals, which arise in the study of optics. There are two such integrals: S(z) := sin(t2) at and C(z) := cos(t? ) at A. [6 pts] Use the Taylor series for cos(t) and the rules discussed in class to show that the Taylor series for C(x) = cos(t2) dt centered at z = 0 is (-1) k24k+1 (4k + 1) . ( 2k) ! In order to earn full credit, show your work in K = 0 summation notation and perform all calculations by hand