use geometry/interpreting in terms to evaluate:

Question

6 -2 x<-3

f(x)dx ; f is defined by : f(x)={ sqrt.(9-x²) -3≤x≤3

5 2x-6 x>3

Answer 1

If the function is:

and the integral is between 5 and 6, then you only need to worry about f(x) = 2x - 6:

The the integral is the area of the trapezoid shown between x = 5 and x = 6.

A_Trapezoid = 1/2(b₁ + b₂)h = 1/2(4 + 6)(1) = 5