Bài tập Toán INTEGRATION PRACTICE 10

The curve meets the straight line at the points A and B.. The point P is located on the x axis so that the straight line segment BP is parallel to the y axis... The finite region R , sho

Question 27 (***)

The figure above shows the graph of the curve C with equation

2

y=x − x+ , x ∈ » intersected by the straight line L with equation

3

y= x , x ∈ » The curve meets the straight line at the points A and B

The point P is located on the x axis so that the straight line segment BP is parallel to the y axis

The finite region R is bounded by C , L , BP and the x axis

Show that the area of R , shown shaded in the figure, is 39

2

proof

2

y=x − x+

x

y

O

R

P

B

A

3

y= x

Question 28 (***)

The figure above shows the graph of the curve with equation

5

14 33

f x

x

−



=

≥

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 area of R

90

x

y

O

R

B A

( )

y= f x

Question 29 (***+)

The diagram below shows a parabola and a straight line with respective equations

2

11 24

y= −x + x− and y =4

The points P and Q are the intersections between the parabola and the straight line

Find the exact area of the shaded region, bounded by the curve, the coordinate axes and the straight line with equation y =4

83 area

6

=

2

11 24

y= −x + x−

4

y = P

x

Q

O y