The point P is the point where C meets the y axis so that the straight line L1 is the normal to C at P.. a Find an equation for L1.. The finite region R , shown shaded in the figure abov
Trang 1The figure above shows the graph of the curve C with equation
2
2
y= x − x+
The point P is the point where C meets the y axis so that the straight line L1 is the normal to C at P
a) Find an equation for L1
The point ( )3,9
2
Q lies on C and the straight line L2 is the normal to C at Q
The finite region R , shown shaded in the figure above, is bounded by L1, L2 and C
b) Find the area of R
2
y= x+ , 15
4
x
y
O
R
2
2
y= x − x+ 1
L
Q
2
L P
Trang 2The figure above shows the graph of the curve C with equation
5
2 8
y=x − x, x ≥0 The curve meets the x axis at the origin O and at the point A
The tangent to C at O is denoted by L1 and the tangent to C at A is denoted by L2
The finite region R , shown shaded in the figure above, is bounded by C, L1 and L2
Determine the area of R
384 11.0
35 ≈
1
L
x
y
O
5
2 8
y=x − x
R
2
L
A
Trang 3The figure above shows the curve C with equation
2
5 4
y= + x−x , intersected by the horizontal straight lines with equations y =5 and y =8
Calculate the exact area of the shaded region, bounded by C and the two straight lines
28 area
3
=
2
5 4
y= + x−x
5
y =
8
y =
x y
O