Question

Approximate the double integral of f(x,y)=x+y over the rectangle R located between the lines x=−1,x=1,y=0 and y=1 (a) Using the partition x=−1,0,1 and y=0, 21​ ,1 with (x k​ ,y k​ ) the upper right corner of the k th subrectangle. ∬ R​ f(x,y)dA≈ (b) Using the partition x=−1,− 21​ ,0, 21​ ,1 and y=0, 41​ , 21 , 43​ ,1 with (x k​ ,y k​ ) the upper right corner of the k th subrectangle. ∬ R​ f(x,y)dA≈

Answer 1

To approximate the double integral of f(x,y)=x+y over a rectangle, use the given partitions and upper right corners of the sub rectangles.

Step-by-step explanation:

To approximate the double integral of f(x,y)=x+y over the rectangle R, we can use the given partitions and upper right corners of the sub rectangles.

(a) Using the partition x=−1,0,1 and y=0, 2/1​ ,1, the double integral is approximated by the sum of the function values at the upper right corners of each sub rectangle multiplied by the area of each sub rectangle.

(b) Using the partition x=−1,− 2/1​ ,0, 2/1​ ,1 and y=0, 4/1​ , 2/3​ , 1, the double integral is approximated likewise.