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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



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