Question

Find the area of the region included between.
Y=2x² of the line y = 4x​

Answer 1

Answer:

Given curve is y=2x−x

2

−y=x

2

−2x

−y+1=x

2

−2x+1

−(y−1)=(x−1)

2

Which represents a downward parabola with vertex at (1,1)

Point of intersection of the parabola and the line y=x

Put y=x

−(x−1)=(x−1)

2

−x+1=x

2

−2x+1

⇒x

2

−x=0

x(x−1)=0

⇒x=0,1

∴ Points of intersections are (0, 0) and (1, 1).

∴ The area enclosed between the curve y=2x−x

2

and the line y = x

∫

0

1

(2x−x

2

−x)dx=∫

0

1

(x−x

2

)dx=[

2

x

2

−

3

x

3

]

0

1

=(

2

1

−

3

1

)−(0−0)=

6

1

sq. unit.