Bài tập Toán INTEGRATION 13

Created by T. Madas
Question 36

(***+)
y
M

y = 4 x − x2
O
A

x

The figure above shows the curve with equation

y = 4 x − x2 , x ∈ » .
The point M is the maximum point of the curve and the point A is one of the x
intercepts of the curve.
Find the exact area of the shaded region, bounded by the curve and the straight line
segment joining A and M .

area = 4
3

Created by T. Madas


Created by T. Madas
Question 37

(***+)

y

f ( x ) = x2 − 2 x + 2

O

1

4

x

The curve C has equation

f ( x ) = x2 − 2 x + 2 , x ∈ » .

a) Find the area of the finite region bounded by C , the x axis and the straight
lines with equations x = 1 and x = 4 , shown shaded in the figure above.
b) Hence evaluate



4

2 f ( 5 − x ) dx .

1

12 , 24

Created by T. Madas


Created by T. Madas
Question 38

(***+)

y

y = x2 − 4 x + 8

M

x

O

The figure above shows the curve with equation

y = x2 − 4 x + 8 , x ∈ » .
The point M is the minimum point of the curve.
Find the area of the shaded region, bounded by the curve, the y axis and the straight
line segment from O to M .
area = 20
3

Created by T. Madas