Chapter 6.4, Problem 246E

The following exercises deal with Fresnel integrals.

246. [T] The Fresnel integrals are used in design applications for roadways and railways and other applications because of the curvature properties of the curve with coordinates (C(t). S(r)). Plot the curve (C50, S₅₀) for 0 $\le$t $\le$2 $\pi$ , 247. Estimate ${\displaystyle {\int }_0^{1/4}\sqrt{x-x^2}dx}$ by approximating $\sqrt{1-x}$ using the binomial approximation $1-\frac{x}{2}-\frac{x^2}{8}-\frac{x^3}{16}-\frac{5x^4}{2128}-\frac{7x5}{256}$ .