A rectangular plate 0 ≤ x ≤ 3, 0 ≤ y ≤ 2 has uniform density 5 kg/m². Using ∬ 5 dA, find its mass in kg.

Practice question · Numerical answer

A rectangular plate $0 \le x \le 3$ , $0 \le y \le 2$ has uniform density 5 kg/m². Using $\iint 5\,dA$ , find its mass in kg.

Hints

With a constant integrand, the double integral is just (value) × (area of region).
Area $= 3 \times 2$ .

Show the answer

30 (answers within ±0.1 count)

Why

Mass $= 5 \times 6 = 30$ kg. Constant integrands turn integrals into multiplication, always the first sanity check before attempting harder iterated integrals: does the answer reduce to base × height reasoning?

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A rectangular plate 0≤x≤30 \le x \le 30≤x≤3, 0≤y≤20 \le y \le 20≤y≤2 has uniform density 5 kg/m². Using ∬5 dA\iint 5\,dA∬5dA, find its mass in kg.

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More questions on Double Integrals

A rectangular plate $0 \le x \le 3$ , $0 \le y \le 2$ has uniform density 5 kg/m². Using $\iint 5\,dA$ , find its mass in kg.