Question

Area in between curves:

Answer 1

I know the intercepts are 0, 3 and 4.. would I integrate from 0 to 4?

Answer 2

I would say integrate from 0 to 3, do the same for 3 to 4. Then you can try doing the sum of the absolute values of the integrals (unless certain bounds have been set)

Answer 3

And it's always top curve minus bottom curve right?

Answer 4

Yes

Answer 5

Alright, thank you ~

Answer 6

Here is a plot
notice that there is some ambiguity, unless they gave the x limits

Answer 7

If you call the area from x=0 to 3 positive, the area from x=3 to 4 would (by convention) be negative.

Answer 8

Btw intercepts are 0, 2, 4

Answer 9

Why do we care about intercepts? Don't we need intersections?

Answer 10

It never gave any restrictions so I just wanted to make sure where to go to and from where. And yea, sorry, I confuse interceptions and intersections alot..

Answer 11

integrate from x=0 to 4

the top curve is the cubic, and the bottom curve is the quadratic

Answer 12

the area is sum of rectangles of height h= top curve - bottom curve, and width dx

Answer 13

Thus, do [0,3] and [3,4] separately, since a different function is greater on these two sections.

If you get 32/3, something has gone horrible wrong.

Answer 14

after a quick google,
you want the absolute value of each region (0 to 3) and 3 to 4
added together.

Answer 15

Alright, thanks you 3 :)