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Example 8
Find the area bounded
by the curve y² = 2y - x and y axis.
Solution:
The equation of
the given curve is y² = 2y - x
|
y
|
0
|
1/2
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1
|
3/2
|
2
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x
|
0
|
3/4
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1
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3/4
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0
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Plot the points
(0,0); 
; (1, 1); 
; (0, 2 ) to obtain a rough sketch of the curve.
Thus, the curve
looks like
The curve meets
y axis at the points where x = 0.
That is, we get x=0 in the equation and solve
for y.
2y - y² =
0 Þ
y(2 - y) = 0
Þ
y = 0 or y = 2
\
Required Area =
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