Question

15.2 Double integrals over general regions: Problem 1 Previous Problem Problem List Next Problem (1 point) Calculate the Riemann sum for f(x, y) = 7x – 2y and domain D in Figure 2 with two choices of sample points, and o. Which do you think is a better approximation to the integral of fover D? Why? y 4 O o o 3 o 2 1 O 0 1 2 3 FIGURE 2 S3,4) = $3,4) =

PLEASE ANSWER BOTH AND SHOW WORK FOR A RATING. THANK YOU!

Answer 1

78 is correct. As f is linear function. Therefore mid point sum will give exact answer.

S_{​​​​​3,4}(o)=78 is exact answer or better approximation.

= 15.2)(1) AA = 1x1 = 1 53,4 (*) It(11) + +11,27 + +11,3.) + +11,4)*+ +12,1) + +12,2) + +12,3)+ +1214) + +13,1) + +13,2) + +13,3)++(3,4)] :=1108 + - - $3,4 (0) = f(ži)++11,3)++11, {)++ě, ž) +7( 3 ) + tt) + = 178 1 :) hom D: y 5*34 os y < 2. Y 1p36x?y dĄ = 1*j*30x3y dx dy J2 9xy 1,* dy = Jó [2567-ys] [12842-46/6]= 14512 11 g