Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f(x) = 7 and the interval [a, x] = [6, x].
A) 7(x - 6)
B) 7(x + 6)
C) 7x
D) 42
E) 7

Question

Quizplus · Accepted Answer

The area between a function f(x) and the x-axis over an interval [a, x] can be found using the formula A(x) = ∫f(x)dx from a to x. In this case, f(x) = 7 and the interval is [6,x]. 
So, A(x) = ∫7dx from 6 to x. 
A(x) = 7(x-6) 
Therefore, the area under function A(x) that gives the area between f(x) = 7 and the interval [6, x] is 7(x-6), which is choice A.

Use a Simple Area Formula from Geometry to Find the Area