questions below:

Which do you think will be larger, the average value of f(x,y) = xy over the square 0 S x S 19, 0 S y s 19, or the average value of f over the quarter circle x2 + y2 S 361 in the rst quadrant? Calculate them to nd out. Choose the correct answer below. O A. 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 B. 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. O C. 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. O D. The average value of f over the square 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 less than the area of the square. What is the formula for the average value of f over R? 1 O A. Average value= WIIW dA R O B. Average value= IL]? dA R 1 O C. Average value= fdA area of R R O D. Average value= J'J'f dA R What is the average value of f over the square? The average value is E. (Type an exact answer.) What is the average value of f over the quarter circle? The average value is E. (Type an exact answer.) Describe the given region in polar coordinates. R: |s rs , s e 5 (Type exact answers, using 1: as needed.) Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. Va ,2 a x2 dy dx - a a 2 2 . . . Change the Cartesian integral into an equivalent polar integral. a 2 Va dy dx = dr de - a 2 0 0 a The value of the double integral is (Type an exact answer, using it as needed.)