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Most Important Selected Qs for JEE AdvancedMathematicsArea Under Curves

Paragraph: Consider the differential equation e ^ x ( ydx - dy )= e ^ - x ( ydx + dy ) . Let y =f( x ) be a particular solution to this differential equation which passes through the point (0,2) Let C y= _ 1 4 (x- 1 4 )+ 1 2 ₄ (16 x^2-8 x+1 ) , be another curve. On the basis of above information, answer the following questions : Question: The area bounded by the curve C, parabola x=y^2+ 1 4 and the line x= 1 4 is -

Options

  1. A1
  2. B3
  3. C2 3
  4. D1 3

Correct answer

D. 1 3

Step-by-step solution

y= _ 1 4 (x- 1 4 )+ 1 2 ₄ (16) (x- 1 4 )^2 = _ 1 4 (x- 1 4 )+1- _ 1 4 (x- 1 4 ) y=1 x 1 4 A = ₀^1 ( y ^2+ 1 4 - 1 4 ) dy = 1 3

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