P1^
6
Area as the limit of a sum
ACTIVITY 6.2 Figure 6.13 shows the region bounded by the graph of y = x + 3, the x axis and the
lines x = a and x = b.
(i) Find the shaded area, A, by considering it as the difference between the two
trapezia shown in figure 6.14.
(ii) Show that the expression for A you obtained in part (i) may be written as
x x
a
2 b
2
+ 3
.
(iii) Show that you obtain the same answer for A by integration.
O a b x
3
y
y = x + 3
Figure 6.13
O a b x
3
b + 3
y
y = x + 3
O a x
3
y
y = x + 3
a + 3
Figure 6.14