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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.

Respuesta :

We have

[tex]\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[/tex]

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

[tex]\int_0^5 f(x)\; dx - \int_0^5 3\; dx = 48.787 - 15 = 33.787[/tex]