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Consider the area under the curve y = 2x 1 over the interval [0, 4].

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Final answer:

To calculate the area under the curve y = 2x - 1 over the interval [0, 4], use integration to find the antiderivative of the function and evaluate the definite integral.

Step-by-step explanation:

To calculate the area under the curve y = 2x - 1 over the interval [0, 4], we can use integration. First, find the antiderivative of the function: F(x) = x^2 - x. Then, evaluate the definite integral from 0 to 4: A = ∫(0 to 4) (2x - 1) dx = [x^2 - x] from 0 to 4 = (4^2 - 4) - (0^2 - 0) = 16 - 4 = 12. Therefore, the area under the curve over the interval [0, 4] is 12 square units.

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