Using MATLAB

3. The integrals Si(a)dt and Ce)-,cos( )dt sin 0 0 are called Fresnel integrals and are studied in optics. (a) Use the first four terms of the Maclaurin series for each function to approximate (b) How many terms are required to approximate s(0.05) with an error no greater (c) How many terms are required to approximate C(-0.25) with an error no greater each of these integrals. than 104? What is S(0.05) approximately equal to using this many terms? than 10-0? What is C(-0.25) approximately equal to using this many terms? (d) Using these integrals as parametric equations defines a curve clled an Euler spiral whose coordinates are given by (C(r). S(a)). Produce a graph using plot for n in the interval [-10, 10) using a step size of 001. It will probably take a minute or two for MATLAB to evaluate the function at that many points. (Caution: you need to use the integral definitions and not Taylor polynomial approximations.)