Exercise · ZW-DOUBLE-INTEGRAL-007 · ★★☆ Intermediate
On a region \(D\) of area \(6\) it is known that \(\iint_D f\,dA=24\). What is the average value of \(f\) on \(D\)?
Choose one option.
Show answer
- D. \(4\)
Explanation
The average value is \(\dfrac{1}{\text{area}(D)}\iint_D f\,dA=\dfrac{24}{6}=4\).
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 \(D\).
\[\iint_D f(x,y)\,dA=\lim_{\max\Delta A_i\to0}\sum_i f(x_i^*,y_i^*)\,\Delta A_i\]
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