1. Consider the following integral: 0/4sec2secr3(1cos2)er2sin2drd (a) Draw the region of integration R for the above integral. Describe the region in rectangular coordinates ( x,y ) with a set of inequalities (hint: break the region into two easy sub-regions and give inequalities for each). (b) What is the infinitesimal area unit for polar coordinates? Removing the infinitesimal area, what is the remaining integrand for the integral above? What is the infinitesimal area unit for rectangular coordinates? (c) Convert the given integral into a set of iterated integrals in rectangular coordinates (hint: use the half-angle/double-angle identities for sine and cosine). (d) Evaluate the your integral from part (c). I recommend integrating with respect to x first