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Bài tập CALCULUS 09
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Created by T. Madas
Question 34
(**+)
y
y = x+3
y = 9 + 2 x − x2
R
B
A
x
O
The figure above shows the graph of the curve C with equation
y = 9 + 2 x − x2 ,
and the straight line L with equation
y = x+3.
The curve meets the straight line at the points A and B .
The finite region R , shown shaded in the figure, is bounded by the curve C , the
straight line L and the coordinate axes.
Show that the area of R is 13.5 square units.
SYN-A , proof
Created by T. Madas
Created by T. Madas
Question 35
(**+)
A curve has equation
y = x3 − 10 x + 2 , x ∈ » .
The point P ( 2, −10 ) lies on the curve.
The straight lines l1 and l2 are the tangent and the normal to the curve at P ,
respectively.
a) Find an equation for l1 and an equation for l2 .
l1 crosses the x axis at A and l2 crosses the y axis at B .
b) Find the area of the triangle OAB where O is the origin.
C1C , y = 2 x − 14 , 2 y + x + 18 = 0 , area = 31.5
Created by T. Madas
Created by T. Madas
Question 36
(**+)
By showing clear workings, find the value of
9
1
6 x−
6
dx .
x
C2I , 80
Question 37
(**+)
Find the value of the constant k , k > 1 , given that
k
4 x − 3 dx = 28 .
1
k=9
2
Created by T. Madas
