Use a simple area formula from geometry to find the area under function A(x) that gives the area under the function f(x) = 9 on the interval [2, x].
use simple area formula from geometry to find the area function A(x).Confirm that A'(x)=f(x) where f(x)=3x-3. ;. [a,x]=[2,x]
To find the area under a function, we can use the formula for the area of a rectangle, which is base multiplied by height. In this case, the base will be the difference between the x-coordinates, and the height will be the value of the function at each point.
Given function f(x) = 9 on the interval [2, x], let's call the desired area A(x). To find A(x), we first need to find the difference in x-coordinates. In this case, the lower limit of integration is fixed at 2, so the base will be (x - 2).
The height of the rectangle represents the value of the function at each point, which is a constant 9 throughout the interval. Therefore, the height is simply 9.
Now we can use the area formula: A(x) = base * height.
Substituting the values, we get:
A(x) = (x - 2) * 9
So, the area under the function A(x) on the interval [2, x] is given by the formula A(x) = 9(x - 2).