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NEED HELP The following table gives the measured height f(x, y) (in ft.) at 1 ft

ID: 2841539 • Letter: N

Question

NEED HELP

The following table gives the measured height f(x, y) (in ft.) at 1 ft. intervals in a pile of gravel in the rectangle R = [0, 6] x [0, 4] x = 0 1 2 3 4 5 6 y = 0 0.4 0.4 0.6 0.8 0.6 0.6 0.2 y = 1 0.8 1.6 1.8 2.5 2.1 0.8 0.1 y = 2 0.5 1.5 3.2 3.5 2.1 0.6 0.1 y = 3 0.4 0.8 1.3 1.5 1.4 0.6 0.4 y = 4 0.3 0.3 0.5 0.8 0.5 0.4 0.2 Estimate the volume using the midpoint rule in a double Riemann sum with m = 3 subdivisions along the x-axis and n = 2 subdivisions along the y-axis. Show the exact terms in this sum before you perform any arithmetic, and then show the final sum. Modify your sum in part (a) to estimate the integral and compute the final sum.

Explanation / Answer

(6-0)/3*(4-0)/2*(f(1,1)+f(3,1)+f(5,1)+f(1,3)+f(3,3)+f(5,3)) =

2^2*(1.6+2.5+0.8+0.8+1.5+0.6)=31.2


b) (6-0)/3*(4-0)/2*( 1f(1,1)+3f(3,1)+5f(5,1)+1f(1,3)+3f(3,3)+5f(5,3))=

2^2*(1*1.6+3*2.5+5*0.8+1*0.8+3*1.5+5*0.6)=85.6