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Bài tập Toán INTEGRATION PRACTICE 03
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Created by T. Madas
Question 6
(**)
y
y = x3 − 8 x 2 + 16 x
R
O
A
x
The figure above shows the cubic curve with equation
y = x3 − 8 x 2 + 16 x , x ∈ » .
The curve meets the x axis at the origin O and at the point A .
a) Show clearly that x = 4 at A .
The finite region R is bounded by the curve and the x axis.
b) Find the exact area of R .
64
3
Created by T. Madas
Created by T. Madas
Question 7
(**)
y
y = x 4 − 8 x + 11
11
R
O
2
x
The figure above shows the curve with equation
y = x 4 − 8 x + 11 , x ∈ » .
The point with coordinates ( 2,11) lies on the curve.
The finite region R is bounded by the curve and the straight line with equation y = 11 .
Show that the area of R , shown shaded in the figure, is 9.6 square units.
proof
Created by T. Madas
Created by T. Madas
Question 8
(**)
y = x3 − 12 x 2 + 45 x − 34
y
B
R
A
O
1
4
x
The figure above shows the curve with equation
y = x3 − 12 x 2 + 45 x − 34 .
The points A and B lie on the curve, where x = 1 and x = 4 , respectively.
The finite region R is bounded by the curve and the straight line segment AB .
Show that the area of R , shown shaded in the figure, is exactly 81 .
4
proof
Created by T. Madas
