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Bài tập Toán INTEGRATION 19
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Created by T. Madas
Question 54
(****)
y
y = 1 x2 − 2 x + 6
2
P
L1
R
Q
L2
O
x
The figure above shows the graph of the curve C with equation
y = 1 x2 − 2 x + 6 .
2
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 Q 3, 9 lies on C and the straight line L2 is the normal to C at Q .
2
The finite region R , shown shaded in the figure above, is bounded by L1 , L2 and C .
b) Find the area of R .
y = 1 x + 6 , 15
4
2
Created by T. Madas
Created by T. Madas
Question 55
(****+)
5
y
y = x 2 − 8x
A
O
x
R
L1
L2
The figure above shows the graph of the curve C with equation
5
y = x 2 − 8x , 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
Created by T. Madas
Created by T. Madas
Question 56
(****+)
y
y = 5 + 4 x − x2
y =8
y =5
x
O
The figure above shows the curve C with equation
y = 5 + 4 x − x2 ,
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.
area = 28
3
Created by T. Madas
