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MHT CET202211 Aug 2022Morning ShiftMathematicsVector AlgebraActual

₀^1 8 (1+x) 1+x^2 ~d x=

Options

  1. A2 2
  2. B2
  3. C- 2
  4. D- 2 3

Correct answer

B. 2

Step-by-step solution

aligned & let x= & d x= ^2 d , when x=0, =0 ; when x=1 , & = 4 aligned I= ₀^ 4 8 (1+ ) 1+ ^2 ^2 d = ₀^ 4 8 (1+ ) d ( i ) I = ₀^ 4 8 (1+ ( 4 - ) d [ ₀^a f(x) d x= ₀^a f(a-x) d x ] . [ ( 4 - )= 1- 1+ ] from (i) +( ii ) aligned & 2 I= ₀^ / 4 8 (1+ ) 2 (1+ ) d & 2 I =8 ₀^ / 4 2 ~d =8 2[ ]₀^ / 4 =8 2 4 aligned I = 2

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