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Bài tập CALCULUS 71
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Created by T. Madas
Question 244
(****+)
y
y = 5 + 4 x − x2
y =8
y =5
x
O
The figure above shows the curve C with equation
y = 5 + 4 x − x2 ,
intersected by the horizontal straight lines with equations y = 5 and y = 8 .
Calculate the exact area of the shaded region, bounded by C and the two straight lines.
C2O , area = 28
3
Created by T. Madas
Created by T. Madas
Question 245
(****+) non calculator
1
+5 x , x > 0.
x
y=
Show clearly that
4
y
3
dx = 1931 .
1
proof
Created by T. Madas
Created by T. Madas
Question 246
(****+)
y
O
y = x 2 − 14 x + 48
L1
Q
P
x
R
S
L2
The figure above shows the curve with equation
y = x 2 − 14 x + 48 .
The curve crosses the x axis at the points P ( x1, 0 ) and Q ( x2 ,0 ) , where x2 > x1 .
The tangent to the curve at Q is the straight line L1 .
The tangent to the curve at some point R is denoted by L2 .
Given further that L1 meets L2 at right angles, find the coordinates of the point of
intersection between L1 meets L2 , denoted in the figure by S .
(
MP1-L , S 59 , − 5
8
4
Created by T. Madas
)
