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KCET2020MathematicsDifferential Equations

The area of the region bounded by the curve y²=8 x and the line y=2 x is

Options

  1. A16 3 sq. units
  2. B4 3 sq. units
  3. C3 4 sq. units
  4. D8 3 sq. units

Correct answer

B. 4 3 sq. units

Step-by-step solution

Given equation of curve, y²=8 x and line y=2 x Now, intersecting points of given curve and line. aligned & (2 x)²=8 x & 4 x²=8 x & x=0,2 & Putting values of x in y=2 x then, we get y=0,4 & Required area of bounded region. aligned = ₀²( 8 x -2 x) d x= ₀² (2 2 x^ 1 / 2 -2 x ) d x=2 ₀² ( 2 x^ 1 / 2 -x ) d x=2 [ 2 ₀² x^ 1 / 2 d x- ₀² x d x ]=2 [ 2 ( x^ 3 / 2 3 / 2 )₀²- ( x² 2 )₀² ]=2 [ 2 2 3 (2)^ 3 / 2 -2 ]=2 [ 8 3 -2 ]=2 ( 2 3 )= 4 3 sq. units

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