Question

Find the area or the region bounded by the curves y = x3 and y = 9x.

0
10.13
40.50
20.25

Answer 1

I have graph the functions

Answer 2

they intersect at (0,0)

Answer 3

Graph of the two functions

Answer 4

the regions you want are in blue

Answer 5

sorry I mixed up my color coding. Not sure how that happened

Answer 6

where else do the graphs cross @Trisarahtops ?

Answer 7

oh I see at (3,27)

Answer 8

where else?

Answer 9

(-3,-27)

Answer 10

the blue region is in 2 symmetric pieces. To find the area of the whole blue region, find the area of the upper half, then double it

Answer 11

f(x) = 9x
g(x) = x^3

\[\Large \text{area of upper half} = \int_{0}^{3}\left[f(x) - g(x)\right]dx\]

Answer 12

since f(x) is the upper function on the interval from x = 0 to x = 3

Answer 13

I got 20.25. And doubled would be 40.5 @jim_thompson5910

Answer 14

40.5 is the correct final answer

Answer 15

Thank you

Answer 16

no problem