Exercise · ZW-DOUBLE-INTEGRAL-003 · ★☆☆ Basic
Divide \(R=[0,2]\times[0,2]\) into four squares of side \(1\) and compute the Riemann sum of \(f(x,y)=x+y\) taking the upper-right corner of each square.
Choose one option.
Show answer
- D. \(12\)
Explanation
The points are \((1,1)\), \((2,1)\), \((1,2)\), \((2,2)\), with values \(2,3,3,4\) (sum \(12\)). Each square has \(\Delta A=1\), so the sum is \(12\). With the lower-left corner it would be \(4\).
Review the concept: Double integral
The double integral of a function \(f\) over a region \(D\) of the plane is the limit of the sums of the values of \(f\) times the area \(\Delta A\) of ever finer cells covering \(D\).
\[\iint_D f(x,y)\,dA=\lim_{\max\Delta A_i\to0}\sum_i f(x_i^*,y_i^*)\,\Delta A_i\]
More practice problems: double integral
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