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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

If f'(x) = f(x) + ∫_0^1 f(x)dx and given f(0) = 1 , then ∫ f(x)dx...

If f′(x)=f(x)+∫01f(x)dxf'(x) = f(x) + \int_0^1 f(x)dx and given f(0)=1f(0) = 1, then ∫f(x)dx\int f(x)dx is equal to: *(where CC is an arbitrary constant.)*

Options

  1. A23−eex+(3−e1−e)x+C\frac{2}{3-e}e^x + \left(\frac{3-e}{1-e}\right)x + C
  2. B23−eex+(1−e3−e)x+C\frac{2}{3-e}e^x + \left(\frac{1-e}{3-e}\right)x + C
  3. C32−eex+(1+e3+e)x+C\frac{3}{2-e}e^x + \left(\frac{1+e}{3+e}\right)x + C
  4. D22−eex+(1−e3+e)x+C\frac{2}{2-e}e^x + \left(\frac{1-e}{3+e}\right)x + C

Correct answer

B. 23−eex+(1−e3−e)x+C\frac{2}{3-e}e^x + \left(\frac{1-e}{3-e}\right)x + C

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