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MHT CET202014 Oct 2020Morning ShiftMathematicsDefinite IntegrationActual

₀¹ ⁻¹ ( 2 x 1-x² ) d x=

Options

  1. A- 2
  2. B2 - 2
  3. C+ 2
  4. D2 + 2

Correct answer

B. 2 - 2

Step-by-step solution

Let I= ₀¹ ⁻¹ ( 2 x 1-x² ) d x Put x= d x= ² d When x=0, =0 and when x=1, = 4 I = ₀^ 4 [ ⁻¹ ( 2 1- ² ) ] (1+ ² ) d = ₀^ 4 ⁻¹( 2 ) (1+ ² ) d = ₀^ 4 2 ² d =2 ₀^ / 4 ² d =2[ ]₀^ / 4 -2 ₀^ / 4 d =2 [ 4 ]+2[ | |]₀^ / 4 = 2 +2 [ | 1 2 | ]= 2 +2 (2)^ 1 2 = 2 - 2

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