Exercise · ZW-DOUBLE-INTEGRAL-005 · ★☆☆ Basic
If \(\iint_D f\,dA=3\) and \(\iint_D g\,dA=5\), what is \(\iint_D (2f-g)\,dA\)?
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- C. \(1\)
Explanation
The integral is linear: \(\iint_D(2f-g)\,dA=2\iint_D f\,dA-\iint_D g\,dA=2\cdot3-5=1\). The integrals are not multiplied, and the coefficients are not dropped.
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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