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JEE Main20252 Apr 2025Evening ShiftMathematicsDefinite IntegrationActual

Let (a, b) be the point of intersection of the curve x^2=2 y and the straight line y-2 x-6=0 in the second quadrant. Then the integral I= _a^b 9 x^2 1+5^x d x is equal to :

Options

  1. A24
  2. B27
  3. C18
  4. D21

Correct answer

A. 24

Step-by-step solution

aligned & x^2=2 y & y=2 x+6 & x^2=4 x+12 aligned .x^2-4 x-12=0 gathered x=6 y=18 gathered , gathered if x=-2 y=2 gathered (6,18) &(-2,2) Here (6,18) Rejected because (a, b) lies in 2^ nd quadrant aligned & a =-2 & ~b =2 & I = _ -2 ^2 9 x ^2 1+5^ x dx = _ -2 ^2 9 5^ x x ^2 1+5^ x dx & 2 I = _ -2 ^2 9 x ^2 dx =18 ₀^2 x ^2 dx =18 ( x ^3 3 )₀^2 & 2 I =48 & I =24 aligned

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