Problem 10: The theory of optics gives rise to the two Fresnel integrals S(x) = [*sin(t2) dt and C(x) = Scos(t2) dt. a) (2 pts) Use the Maclaurin series for f(x) = sin(x) in the table at the end of the exam to expand sin( t2) in a Maclaurin series. (Do not recreate the Maclaurin series using the definition of Taylor series and derivatives.) b) (2 pts) Integrate to find the first four nonzero terms of the Maclaurin series for S(x) that you found in (a). c) (2 pts) Use the polynomial in (b) to approximate S(1) = So sin(t2) dt