The point M is the maximum point of C and the point A has coordinates 0,12.. Find the exact area of the shaded region, bounded by the curve, the y axis and the straight line segment from
Trang 1The figure above shows the graph of the curve C with equation
2 4
y= x−x , x ∈»,
intersected by the straight line L with equation
3 6
y= x− , x ∈»
As shown in the above figure, C meets L at the points A and B , and crosses the x
axis at the origin O and at the point P
The finite region R is bounded by C , L and the x axis
Show that the area of R , shown shaded in the figure, is 19
6
proof
2 4
y= x−x
x
B
A
Trang 2The figure above shows the curve C with equation
(6 )
y=x −x , x ∈ »
The point M is the maximum point of C and the point A has coordinates (0,12)
Find the exact area of the shaded region, bounded by the curve, the y axis and the straight line segment from A to M
27 area
2
=
x
O
M
(6 )
y=x −x
Trang 3The figure above shows the quadratic curve with equation
2 8
y= x−x , x ∈»
The point M is the maximum point of the curve and the point A is one of the curve’s
x intercepts
Find the exact area of the shaded region, bounded by the curve, the x axis and the
straight line segment from A to M
224 area
3
=
2 8
y= x−x
A
M
O
x