The graph of f is shown. Evaluate each integral by interpreting it in terms of areas.

Question

Link to graph : https://ibb.co/tb7yx1C

Find:

(a)    8	f(x) dx
0

(b)    20	f(x) dx
0

(c)    28	f(x) dx
20

(d)    36	f(x) dx
0

Answer 1

Hello James! The graph only goes up to x=18 so I am unsure on how to answer for intervals extending beyond that. But part a can be answered if you mean the integral from x=0 to x=8 of f(x) dx.

We look for the areas between the curve and the x-axis from x=0 to x=8. We can interpret this as a geometry problem. We see if we break it up from x=0 to x=4 and x=4 to x=8 we have two trapezoids.

Trap 1: x=0 to x=4

(2+6)/2*4=16

Trap 2: x=4 to x=8

(2+6)/2*6=24

Thus the total integral is 40 units^2

Hope this helps!