Calculus Question

Question

Let g(x) = x	f(t) dt
0

,

 where f is the function whose graph is shown.

(a) Evaluate g(0), g(4), g(8), g(12), and g(24).

g(0)	=
g(4)	=
g(8)	=
g(12)	=
g(24)	=

(b) On what interval is g increasing? (Enter your answer using interval notation.)

(c) Where does g have a maximum value?

x =  

(d) Sketch a rough graph of g. Which of the following graphs is correct?

Answer 1

g(x) = ∫_{(from 0 to x)} f(t)dt

So, for example,

g(4) = ∫_{(from 0 to 4)}f(t)dt = area below the curve and above the x-axis between x = 0 and x = 4

= (8)(4) = 32

g(16) = ∫_{(from 0 to 16)}f(t)dt = (area below curve and above x-axis from 0 to 12) - (area of region below x-axis and above the curve from 12 to 16)