Find the exact area of the region, bounded by the curve and the x axis, shown shaded in the figure above... Find the range of values of x for which y is decreasing.
Trang 1The figure above shows the curve with equation
(3 )( 1)
y= −x x+ , x∈
Find the exact area of the region, bounded by the curve and the x axis, shown shaded
in the figure above
MP1-M , area 32
3
=
(3 )( 1)
y= −x x+
O y
x
Trang 22 3 3
6
x
= − + , x≠ 0
Find a fully simplified expression for
y dx
C1A , 2 3 3 2 2 4
−
Question 5 (**)
( ) 2
f x = x − x + , x ∈
Find the coordinates of the point on the curve with equation y= f x( ), whose gradient
is 5
(3, 2− )
Trang 33 2
y=x − x + , x∈ Find the range of values of x for which y is decreasing
C2E , 0< <x 4
Question 7 (**)
The figure above shows the curve with equation
( 1)( 2)( 4)
y= x+ x− x− , x∈
a) Write the equation of the curve in the form 3 2
y=x +ax +bx+c, where a , b
and c are constants
b) Find the exact area the shaded region
C2D , y=x3−5x2+2x+8 , area 16
3
=
( 1)( 2)( 4)
y= x+ x− x−
y