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Bài tập Toán INTEGRATION 06
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Created by T. Madas
Question 5
The point P ( 3, −1) lies on the curve with equation y = f ( x ) , whose gradient function
is given by
f ′ ( x ) = 1 − x2 , x ∈ ℝ .
Find an equation for f ( x ) .
f ( x ) = 5 + x − 1 x3
3
Question 6
By showing clear workings, find the value of
∫
9
1
6 x−
6
dx .
x
80
Created by T. Madas
Created by T. Madas
Question 7
The curve C with equation y = f ( x ) has gradient function
dy
7
= 9 x2 + 2 , x ≠ 0 .
dx
x
The point A ( −1, −1) lies on C .
Find an equation for C .
y = 3 x3 −
7
−5
x
Question 8
(
)
y = x 6x − 5 x , x ≥ 0 .
By showing all steps in the workings, find an expression for
∫
y dx .
5
2 x3 − 2 x 2 + C
Created by T. Madas
Created by T. Madas
Question 9
The point P ( 4,9 ) lies on the curve with equation y = f ( x ) , whose gradient function
is given by
f ′( x) = 1+
2
, x >0.
x
Find an equation for f ( x ) .
f ( x) = x + 4 x − 3
Question 10
dy
1
= 4+ 2 , x ≠ 0.
dx
x
Given that y = 5 when x = 1 , express y in terms of x .
y = 4x −
Created by T. Madas
1
+2
x
