Exercise · ZW-DOUBLE-INTEGRAL-001 · ★☆☆ Basic
Compute \(\iint_R 5\,dA\) over the rectangle \(R=[1,4]\times[0,2]\).
Choose one option.
Show answer
- B. \(30\)
Explanation
For a constant \(c\), \(\iint_R c\,dA=c\cdot\text{area}(R)\). The area is \(3\cdot2=6\), so the integral is \(5\cdot6=30\).
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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