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Find the area of the region under the graph of the function f on the interval [−1, 4]. f(x) = 2x 5

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Answer:

Explanation:

To find the area of the region under the graph of the function f(x) = 2x + 5 on the interval [-1, 4], we need to integrate the function over that interval.

The integral of f(x) with respect to x over the interval [-1, 4] gives us the area under the curve.

∫[a,b] f(x) dx denotes the integral of f(x) with respect to x over the interval [a,b].

In this case, we have:

∫[-1,4] (2x + 5) dx

Evaluating this integral, we get:

∫[-1,4] (2x + 5) dx = [x^2 + 5x] evaluated from -1 to 4

Plugging in the upper and lower limits, we have:

= (4^2 + 5(4)) - ((-1)^2 + 5(-1))

= (16 + 20) - (1 - 5)

= 36 + 4

= 40

Therefore, the area of the region under the graph of the function f(x) = 2x + 5 on the interval [-1, 4] is 40 square units.

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