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Bài tập CALCULUS 50
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Created by T. Madas
Question 178
(****)
y = q − 2x
A
B
y = p + 10 x − x 2
C
The figure above shows a curve and a straight line with respective equations
y = p + 10 x − x 2
and
y = q − 2x ,
where p and q are constants.
The curve meets the straight line at the points A and C , and the point B lies on the
curve so that AB is parallel to the x axis.
a) Given the coordinates of C are (10,0 ) find …
i. … the value of p and the value of q .
ii. … the coordinates of A and B .
a) Determine the value of the area of the finite region bounded by the curve and
the straight line segment AB .
SYN-K , p = 0 , q = 20 , A ( 2,16 ) , B ( 8,16 ) area = 36
Created by T. Madas
Created by T. Madas
Question 179
(****)
y = 6 + 6 x + 5x , x ≥ 0 .
Show clearly that
y 2 − x 2 ) dx = 36 x + Px
(
3
2
5
+ 48 x 2 x + Qx 2 + Rx3 + C ,
where P , Q and R are constants to be found, and C is an arbitrary constant.
P = 48 , Q = 24 , R = 8
Created by T. Madas
Created by T. Madas
Question 180
(****)
y=
1 2
−3 , x > 0 .
3 x x
Find the range of values of x for which y is decreasing.
SYN-I , 0 < x < 2
Created by T. Madas
