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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: If the area bounded by the curve y =f( x ) , curve C , ordinate x = 1 4 & the o

Options

  1. An 6
  2. Bn 4
  3. C4
  4. Dn 12

Correct answer

B. n 4

Step-by-step solution

_ 1 / 4 ^a (e^x+e^ -x -1 ) d x=4- 4+ 1 [4] e - [4] e ( e ^ x - e ^ - x - x )_ 1 / 4 ^x=4- 4+ 1 [4] e - [4] e aligned & e ^ a - e ^ - a - a - [4] e + 1 [4] e + 1 4 & =4- 4+ 1 [4] e - [4] e & e ^ a - e ^ - a - a + 1 4 =4- 4 a = n 4 aligned

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