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Example 7
Find the area of
the region bounded by the curves y = x² and
y² = x
Solution:
The points of intersection
of the curves are obtained by solving the system
formed by the equation y = x² and y²
= x
Elimination y,
we obtain
x4 =
x Þ x(x3
- 1) = 0
Þ
x = 0 or x = 1
if x = 0 , then y = 0
and if x = 1 then y = 1
Thus, the curves
intersect at (0, 0) and (1, 1)
The required area
is:
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