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Bài tập Toán INTEGRATION 17
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Created by T. Madas
Question 48
(****)
y
N
M
y = x − 2 x4
O
x
The diagram below shows the quartic curve with equation
y = x − 2 x4 , x ∈ » .
The point M is the maximum point on the curve and the point N lies on the y axis
so that the straight line segment MN is parallel to the x axis.
Find the exact area of the shaded region, bounded by the curve, the y axis and the
straight line segment from M to N .
area = 3
40
Created by T. Madas
Created by T. Madas
Question 49
(****)
y
y = x2 − 4 x + 3
A
O
D
B
C
x
The figure above shows a quadratic curve with equation
y = x2 − 4 x + 3 .
The points A , B and C are the points where the curve meets the coordinate axes.
The point D lies on the curve so that AD is parallel to the x axis.
Calculate the exact area of the shaded region, bounded by the curve, the x axis and the
straight line segment BD .
area = 19
6
Created by T. Madas
Created by T. Madas
Question 50
(****)
y
L
R
O
y = 1 x2 − 9 x + 7
2
2
P
Q
x
The diagram above shows the quadratic curve C with equation
y = 1 x2 − 9 x + 7 .
2
2
The curve crosses the x axis at the points P and Q , and the y axis at the point R .
The line L is the tangent to C at the point P .
a) Find an equation of L .
b) Find the exact area of the shaded region bounded by the tangent at P , the curve
and the y axis.
2 y + 5 x = 10 , area = 4
3
Created by T. Madas
