Exercise · ZW-DOUBLE-INTEGRAL-006 · ★☆☆ Basic
The region \(D\) is the union of two non-overlapping regions \(D_1\) and \(D_2\). If \(\iint_{D_1} f\,dA=7\) and \(\iint_D f\,dA=10\), what is \(\iint_{D_2} f\,dA\)?
Choose one option.
A \(17\) B \(7\) C \(3\) D \(\tfrac{10}{7}\) Show answer ← Back to the question
Explanation By additivity, \(\iint_D f\,dA=\iint_{D_1} f\,dA+\iint_{D_2} f\,dA\). Hence \(\iint_{D_2} f\,dA=10-7=3\).
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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