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Bài tập Toán INTEGRATION 18
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Created by T. Madas
Question 51
(****)
y
O
y=
A
x 4 − 10 x 2 + 9
x2
B
R
x
The figure above shows the graph of the curve with equation
y=
x 4 − 10 x 2 + 9
x2
, x >0.
The curve meets the x axis at the points A and B .
The finite region R , shown shaded in the figure above, is bounded by the curve and
the x axis.
Find the exact area of R .
16
3
Created by T. Madas
Created by T. Madas
Question 52
(****)
y = x2 − 1
y
1
y = 9 1 − 2
x
R
O
x
The figure above shows the graphs of the curves with equations
1
y = x 2 − 1 and y = 9 1 − 2 .
x
The finite region R is bounded by the two curves in the 1st quadrant, and is shown
shaded in the figure above.
Determine the exact area of R .
16
3
Created by T. Madas
Created by T. Madas
Question 53
(****)
y
( 0,1)
x + y =1
R
O
(1,0 )
x
The figure above shows the curve with equation
x + y = 1 , x ∈ » , 0 ≤ x ≤ 1.
The curve meets the coordinate axes at the points (1,0 ) and ( 0,1) .
The finite region R is bounded by the curve and the coordinate axes.
Show that the area of R is 1 .
6
proof
Created by T. Madas
