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Bài tập CALCULUS 73
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Created by T. Madas
Question 249
(****+)
y
y = x 2 + px + 10
B
y = x+q
A
x
O
The figure above shows the graphs of a quadratic curve and a straight line with
respective equations
y = x 2 + px + 10 and
y = x+q,
where p and q are constants.
The curve and the straight line intersect at the points A and B , whose x coordinates
are 1 and 4 , respectively.
Determine the area of the finite region bounded by the curve and the straight line,
shown shaded in the figure.
area = 9
2
Created by T. Madas
Created by T. Madas
Question 250
(****+)
The volume, V cm3 , of a soap bubble is modelled by the formula
2
V = ( p − qt ) , t ≥ 0 ,
where p and q are positive constants, and t is the time in seconds, measured after a
certain instant.
When t = 1 the volume of a soap bubble is 9 cm3 and at that instant its volume is
decreasing at the rate of 6 cm3 per second.
Determine the value of p and the value of q .
C1Z , p = 4 , q = 1
Created by T. Madas
Created by T. Madas
Question 251
(****+)
y
y = 36 − 4 x − x 2
y=x
x
O
The figure above shows the graph of the curve with equation y = 36 − 4 x − x 2 and its
reflection about the straight line with equation y = x .
a) Write down the equation of the curve which is the reflection of the curve with
equation y = 36 − 4 x − x 2 about the straight line with equation y = x .
b) Determine an exact value for the area of the finite region bounded by the curve
with equation y = 36 − 4 x − x 2 , its reflection about the straight line with
equation y = x , and the positive x and y axes.
This region is shown shaded in the figure above.
MP1-I , x = 36 − 4 y − y 2 , AREA = 496 = 165 1
3
3
Created by T. Madas
