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If the integral ∫₀² f(x) dx = -4, determine the value of d such that ∫₀² (-2d²) dx = -4.

1. d = 1
2. d = -1
3. d = ±1
4. None of the above

Correct answer: d = ±1

Solution

Since -2d^2 is constant, the integral from 0 to 2 of -2d^2 dx = -2d^2 * 2 = -4d^2. Setting -4d^2 = -4 gives d^2 = 1, so d = +/-1. The stored answer d=1 omits the valid d=-1, so the correct choice is d=+/-1 (index 2).

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