Use a double integral to find the area of the region inside both the cardioid r= 1 + sin 0 and the cardioid r = 1 + cos 0. Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area inside the cardioid r= 1 + cos 0 until it intersects with r= 1 + sin 0. Notice that because of symmetry, this can be doubled to find the area of the region. 00 S rardo 00Use a double integral to find the area of the region bounded by all leaves of the rose r = 4 cos 70. Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area the leaf that is closest to the positive x-axis. Ayeat = r dr do 10 (Type exact answers, using x as needed.)Sketch the region of integration and evaluate the following integral. -dA, R = {(r,0): 0 sr= 3,x=0=2x} R 4+ 1x2+2 Choose the correct graph below. O A. B. O C. O D. -dA =_ R 4+ 1x2 +2 (Type an exact answer, using it as needed.)Find the average value of -N/ - over the annulus {(r,0): 3 ers 7} The average value is (Type an exact answer.)