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