In (x2 +y2) W Integrate f(x,y) = over the region 1 5x2 + y2 S e 7. 7 The answer is 51m 2 -27: . (Type an exact answer. using 7: as needed. Do not factor.) 11 V121 -x2 Change the Cartesian integral _ _ dy dx into an equivalent polar integral. Then evaluate the polar integral. . . . Change the Cartesian integral into an equivalent polar integral. V 121 -x2 dy dx = ar de (Type exact answers, using it as needed.)Which do you think will be larger, the average value of f(x,y) = xy over the square 0Sx 3, 0Sys 3, or the average value of f over the quarter circle x"+ y-$9 in the first quadrant? Calculate them to find out. O B. The average value of f over the quarter circle will be larger because the average value of f(x,y) increases as the area underneath the function increases. Here, the area of the quarter circle is greater than the area of the square. CC. The average value of f over the square will be larger because the values of f(x,y) increase as both x and y increase. On any line through the origin, values of f(x,y) outside of the quarter circle, but inside the square, will all be greater than or equal to the values inside of the quarter circle. O D. The average value of f over the quarter circle will be larger because the values of f(x,y) decrease as both x and y increase. On any line through the origin, values of f(x,y) outside of the quarter circle, but inside the square, will all be less than or equal to the values inside of the quarter circle. What is the formula for the average value of f over R? A. Average value =- area of R R O B. Average value = | | VF dA R O C. Average value = | |f dA R 1 O D. Average value = area of R IS VF dA R What is the average value of f over the square? The average value is. (Type an exact answer.)