Q7 (5 points) Consider the region above the r-axis and below y = e" with z 2 1, shown below. Consider a wizard hat (infinitely tall) obtained by the solid of revolution obtained by rotating this region about the z-axis. (a) Make a rough sketch of this hat. (b) Does this hat have finite volume? Justify your answer with calculations.Q5 (5 points) Some integrals might seem complicated. But they will simplify significantly if you look at them in the right way. Evaluate the integral F(0) - cos' (8) + sin(20) - 3 cos (0) do sin'(0) + 3 cos3(0) + 2sin(0) - 3 Hint: Try substituting u = sin(0)