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if R = [-1, 3] [0, 2], use a Riemann sum with m = 4, n = 2 to estimate the value of the following. Take the sample points to be the upper left corners of the subrectangles.

int int_R (y^2 - 2x^2) dA

2007-03-28 18:04:07 · 3 answers · asked by bob 3 in Science & Mathematics Mathematics

3 answers

Make a rectangular grid with 1x1 square-base cells whose heights are given by y^2 - 2x^2. The Riemann sum is the total volume of all the cells, which is just the sum of the heights because the areas of the bases are all 1.

x-coord of left edges of rectangles: -1,0,+1,+2
y-coord of top/upper edges: 1, 2

Eight upper-left corners: (-1,1), (-1,2), etc. ....

Here's the calculation I did using matlab. It should be easy to understand even if you don't know matlab.

>> x = -1:2

x = -1, 0 , 1, 2

>> y = 1:2

y = 1 , 2

>> sum = 0;

>> for i=1:4
for j = 1:2
sum = sum + y(j)^2 - 2*x(i)^2
end;
end;

>> sum

sum = -4 (the answer - approximate value of the integral)

2007-03-28 19:56:31 · answer #1 · answered by pollux 4 · 2 0

Riemann Sum Matlab

2016-11-09 21:34:17 · answer #2 · answered by ? 4 · 0 0

assume you elect for to make certain the area between the curves y = x^2 and y = x^3 from x = a million to x= 3. that's complete via the double fundamental Int (x=0 to a million) Int (y = x^2 to x^3) dy dx

2016-11-24 20:57:07 · answer #3 · answered by ? 4 · 0 0

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