Question

Find the area of the region bounded by the curve x = y (2-y) at y-axis.

Answer 1

Answer:

x=4y−y

2

i.e., y

2

−4y=−x

(y−2)

2

=−(x−4)

Which represents a left parabola with vertex at A(4, 2).

The parabola meets Y-axis i.e., x = 0

4y−y

2

=0

i.e., at y=0,4.

The area enclosed between the curve and the Y-axis.

∫

0

4

xdy=∫

0

4

(4y−y

2

)dy

=[4.

2

y

2

−

3

y

3

]

0

4

=[32−

3

64

]−[0,0]=

∣

∣

∣

∣

∣

3

32

∣

∣

∣

∣

∣

sq.unit=

3

32

sq.unit

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