# Find by integration the area of the region bounded by the curve y=2x−x2 and the x-axis.

A

23 sq. units

B

43 sq. units

C

53 sq. units

D

83 sq. units

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## Given equation of curve is y=2x−x2 ⇒x2−2x=−y ⇒x2−2x+1=−y+1 ⇒(x−1)2=−(y−1) This is the equation of parabola having vertex (1, 1) and open downward. The parabola intersect the X-axis, put y = 0, we get 0=2x−x2⇒x(2−x)=0 ⇒x=0,2 ∴ Area of bounded region between the curve and X-axis =∫20ydx =∫20(2x−x2)dx=[2x22−x33]20 =[4−83−0−0]=43 sq units.

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Updated on:21/07/2023

### Knowledge Check

• Question 1 - Select One

## The area of the region bounded by the curve y=2x−x2 and x - axis is

A23 sq , units
B43 sq,units
C53 sq , units
D83 sq. units
• Question 2 - Select One

## The area of the region bounded by the curve y=2x−x2and X- axis is

A23 sq.units
B43 sq.units
C53 sq.units
D83 sq.units
• Question 3 - Select One

## Area of the region bounded by the curve y=x2−5x+4 and the X-axis is

A32
B52
C72
D92

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