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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Let Y= ₀^1 2 x^2+3 x+3 (x+1) (x^2+2 x+2 ) d x . Then which of the following option(s) are equal to Y ?

Options

  1. A4 +2 2- 2
  2. B4 +2 2- 1 3
  3. C2 2- arccot 3
  4. D- 4 +2 2+ arccot 2

Correct answer

D. - 4 +2 2+ arccot 2

Step-by-step solution

Y= ₀^1 2 x^2+3 x+3 (x+1) (x^2+2 x+2 ) By partial fraction decomposition aligned & = ₀^1 ( 2 x+1 - 1 x^2+2 x+2 ) d x= ₀^1 ( 2 x+1 - 1 (x+1)^2+1 ) d x & =2 (x+1)- . (x+1) |₀ ^1 & =2 2- 2+ 4 aligned From (a) A=2 2+ 4 - 2=2 2+ ( 1-2 1+2 )=2 2- arccot 3 (c) From (a) A=2 2+ 4 - 2=- 4 + 4+ 2 - 2=- 4 +2 2+ arccot 2 (d)

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