well, let's find the vertex and intercepts.
x^2 - 11 x = -y - 24
x^2 - 11 x + 121/4 = -y - 24 + 30.25
(x-11/2)^2 = -(y-6.25)
so PN = 6.25
now what are A and B
when y = 0
(x-11/2)^2 = 6.25
x-5.5 = +/- 2.5
x = 3 or 8
A is at 3 and B is at 8
so 2 PN * AB = 62.5
divide by three = 20.83333.....
now the integral
from 3 to 8
of (-x^2 +11 x - 24)dx
-x^3/3 + 11x^2/2 - 24 x
at 8
-10 2/3
at 3
-31.5
20.8333... Whew !
The curve y = 11x - 24 - x^2 cuts the x-axis at points A and B, and PN is the greatest positive value of the y coordinate. Show that 2 PN • AB equals three times the area bounded by that portion of the curve which lies in the first quadrant.
Kinda confused on how to do this
1 answer
4 answers