P1^
6
Exercise(^) 6D
2 (i) Sketch the curves with equations y = x^2 + 3 and y = 5 − x^2 on the same
axes, and shade the enclosed region.
(ii) Find the co-ordinates of the points of intersection of the curves.
(iii) Find the area of the shaded region.
3 (i) Sketch the curve y = x^3 and the line y = 4 x on the same axes.
(ii) Find the co-ordinates of the points of intersection of the curve y = x^3 and
the line y = 4 x.
(iii) Find the total area of the region bounded by y = x^3 and y = 4 x.
4 (i) Sketch the curves with equations y = x^2 and y = 4 x − x^2.
(ii) Find the co-ordinates of the points of intersection of the curves.
(iii) Find the area of the region enclosed by the curves.
5 (i) Sketch the curves y = x^2 and y = 8 − x^2 and the line y = 4 on the same
axes.
(ii) Find the area of the region enclosed by the line y = 4 and the curve y = x^2.
(iii) Find the area of the region enclosed by the line y = 4 and the curve
y = 8 − x^2.
(iv) Find the area enclosed by the curves y = x^2 and y = 8 − x^2.
6 (i) Sketch the curve y = x^2 − 6 x and the line y = −5.
(ii) Find the co-ordinates of the points of intersection of the line and the
curve.
(iii) Find the area of the region enclosed by the line and the curve.
7 (i) Sketch the curve y = x(4 − x) and the line y = 2 x − 3.
(ii) Find the co-ordinates of the points of intersection of the line and the
curve.
(iii) Find the area of the region enclosed by the line and the curve.
8 Find the area of the region enclosed by the curves with equations y = x^2 − 16
and y = 4 x − x^2.
9 Find the area of the region enclosed by the curves with equations y = −x^2 − 1
and y = − 2 x^2.
10 (i) Sketch the curve with equation y = x^3 + 1 and the line y = 4 x + 1.
(ii) Find the areas of the two regions enclosed by the line and the curve.
11 The diagram shows the curve
y = 5 x − x^2 and the line y = 4.
Find the area of the shaded region.
y
O x
y = 5x – x2
y = 4