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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Let f be a differentiable function on R and satisfies f(x) = x^2 +...

Let ff be a differentiable function on RR and satisfies f(x)=x2+∫0xe−tf(x−t)dtf(x) = x^2 + \int_0^x e^{-t} f(x-t) dt; then ∫01f(x)dx\int_0^1 f(x) dx is equal to :

Options

  1. A13\frac{1}{3}
  2. B14\frac{1}{4}
  3. C712\frac{7}{12}
  4. D512\frac{5}{12}

Correct answer

D. 512\frac{5}{12}

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