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.