Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f(x) = x + 7 and the interval [a, x] = [-5, x].

Question

Quizplus · Accepted Answer

The area between the function f(x) = x + 7 and the interval [a, x] can be found by taking the integral of f(x) with respect to x from a to x:
$\int_{a}^{x} (x+7)dx = \frac{(x+7)^2}{2} - \frac{(a+7)^2}{2}$
Substituting a = -5, we get:
$\frac{(x+7)^2}{2} - \frac{(2)^2}{2} = \frac{(x+7)^2-4}{2}$
Simplifying further, we get:
$\frac{(x+7)^2-4}{2} = \frac{x^2+14x+45}{2}$
which is option B.

Use a Simple Area Formula from Geometry to Find the Area