Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f(x) = 4x + 6 and the interval [a, x] = [0, x]. A) 2x² - 6x B) 2x + 6 C) 2x² + 12x D) 4x² + 6x E) 2x² + 6x

Question

Quizplus · Accepted Answer

The area formula for the region between the function f(x) and the interval [a, x] is A(x) = ∫f(x)dx from a to x. In this case, f(x) = 4x + 6 and a = 0. So, A(x) = ∫(4x + 6)dx from 0 to x.
Evaluating the integral, we get A(x) = 2x² + 6x.
Therefore, the answer is E, which matches the formula derived above.

Use a Simple Area Formula from Geometry to Find the Area