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AP EAMCET202125 Aug 2021Evening ShiftMathematicsDefinite IntegrationActual

₀^1 x e^x (x+1)^2 d x is equal to

Options

  1. Ae 2
  2. Be 2 -1
  3. Ce 2 +1
  4. D2e

Correct answer

B. e 2 -1

Step-by-step solution

I= ₀^1 x e^x (x+1)^2 d x aligned I & = ₀^1 e^x [ x (x+1)^2 ] d x & = ₀^1 e^x [ 1 x+1 - 1 (x+1)^2 ] d x aligned Let f(x)= 1 x+1 f^ (x)= -1 (x+1)^2 aligned I & = ₀^1 e^x [f(x)+f^ (x) ] d x I & = .e^x f(x) |₀ ^1 & I= [ e^x x+1 ]₀^1= e 2 -1 aligned

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