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Bài tập Toán INTEGRATION 15
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Created by T. Madas
Question 42
(****)
y
y = 3x − 6
B
O
R
P
x
y = 4 x − x2
A
The figure above shows the graph of the curve C with equation
y = 4 x − x2 , x ∈ » ,
intersected by the straight line L with equation
y = 3x − 6 , 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
Created by T. Madas
Created by T. Madas
Question 43
(****)
y
A
M
y = x(6 − x)
O
x
The figure above shows the curve C with equation
y = x (6 − 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 .
area = 27
2
Created by T. Madas
Created by T. Madas
Question 44
(****)
y
M
y = 8x − x2
O
A
x
The figure above shows the quadratic curve with equation
y = 8x − x2 , 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 .
area = 224
3
Created by T. Madas
