Question

It is known that the function f(x)=3(1.5) ^x has an area of 48.787 units^2"over the interval 0 <=x<=5.If g(x)=f(x)-3, what is A(g, 0<=x<=5)? Explain how you know.

Answer 1

We have

$\displaystyle \int_0^5 g(x)\; dx = \int_0^5 (f(x)-3)\; dx = \int_0^5 f(x)\; dx - \int_0^5 3\; dx$

The first integral is known and it is 48.787. The second integral is the area of a rectangle:

$\int_0^5 f(x)\; dx - \int_0^5 3\; dx = 48.787 - 15 = 33.787$