Math Is Fun Forum

sezza

Guest

Area Between Curves

Find the area between the curves y+8x-8 and y=x^3 - 4x^2 - 7x + 10

Answer is 210.08 units squared

How do you get that?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Area Between Curves

Standard technique for finding areas between two curves y[sub]1[/sub] and y[sub]2[/sub]:

(i) Find the points of intersection between the two curves. (There should be at least two points of instersection.)
(ii) Integrate |y[sub]1[/sub] − y[sub]2[/sub]| between the point of intersection with the lowest x value and the point of intersection with the highest x value.

So the first step for you: Find the points of intersection of

Have you done that?

sezza

Guest

Re: Area Between Curves

yer but there are three points of intersection and i dont know what to do

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Area Between Curves

The points of intersection are at x = −3, 1 and 6. Now calculate |y[sub]1[/sub] − y[sub]2[/sub]| in the two invervals [−3,1] and [1,6].

(i)

(ii)

Hence the area is