Chapter 5.7, Problem 409E

[T] The transformations T : R P. i = 1,.... 4. defined by T₁(u.v) = (u. —v). T₂, (u, v) = (—u. v). T₃ (u. v) = (—u. —v), and T₄(u. v) = (v. u) are called reflections about the

x-axis. y-axis. origin, and the line y = x. respectively.

a. Find the image of the region S = {(u. v)u²+ — v²— 2u -4v +1 $\le$ 0} in the xy- plane through the transformation $T_1\circ T_2\circ T_3\circ T_4$b. Use a CAS to graph R.

c. Evaluate the Integral ${\displaystyle \underset{S}{\iint }\sin \left(u^2\right)dudv}$by using a CAS. Round your answer to two decimal places.