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Bài tập Toán INTEGRATION 12
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Created by T. Madas
Question 33
y
y = f ( x)
O
P ( −1,0 )
Q
x
The figure above shows a curve with equation y = f ( x ) .
The curve meets the x axis at the points P ( −1,0 ) and Q , and its gradient function is
given by
f ′( x) =
8 x3 − 1
x2
, x ≠ 0.
a) Find an equation of the tangent to the curve at P .
b) Find an expression for f ′′ ( x ) .
c) Determine …
i. … an equation of the curve.
ii. … the coordinates of Q .
y = −9 x − 9 , f ′′ ( x ) = 8 + 2 x −3 , y = 4 x 2 +
Created by T. Madas
1
− 3 , Q 1 ,0
2
x
( )
Created by T. Madas
Question 34
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 35
A quadratic curve C passes through the points P ( a, b ) and Q ( 2a, 2b ) , where a and
b are constants.
The gradient at any given point on C is given by
dy
= 2x − 6 .
dx
Find an equation for C , in terms of a .
y = x 2 − 6 x + 2a 2
Created by T. Madas
