If f is a continuous function such that , evaluate .

Question

If f is a continuous function such that , evaluate .

 6 

9 

3 

27

Answer 1

F(x)= integral of f(x) from 2 to 5 = 9

F(x) = integral of 3f(x) from 2 to 5 = ?

try a specific example

f(x) =3x

3f(x) = 9x

F(x) from 2 to 5 = 9 = 3(5) -3(2) = 15-6 =9

F(x) with 3f(x) from 2 to 5 = 9(5)-9(2) = 45-18 = 27

27 = 3 times 9

answer is 27

You might suspect the area is larger. among the choices only 27>9