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KCET2022MathematicsDefinite Integration

₀^1 x e^x (2+x)^3 d x is equal to

Options

  1. A1 27 e- 1 8
  2. B1 27 e+ 1 8
  3. C1 9 e+ 1 4
  4. D1 9 e- 1 4

Correct answer

D. 1 9 e- 1 4

Step-by-step solution

Let Here, 1 (2+x)^2 =f(x) and -2 (2+x)^3 =f^ (x) We know, e^x [f(x)+f^ (x) ] d x=e^x f(x)+c l= [e^x 1 (2+x)^2 ]₀^1= e^x (2+1)^2 - e^0 (2+0)^2 = e 9 - 1 4

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