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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+y) = f(x)f(y) for all x, y and f(0) ≠ 0 , and F(x) =...

If f(x+y)=f(x)f(y)f(x+y) = f(x)f(y) for all x,yx, y and f(0)≠0f(0) \neq 0, and F(x)=f(x)1+(f(x))2F(x) = \frac{f(x)}{1 + (f(x))^2} then :

Options

  1. A∫−20102011F(x)dx=∫02011F(x)dx\int_{-2010}^{2011} F(x) dx = \int_0^{2011} F(x) dx
  2. B∫−20102011F(x)dx−∫02010F(x)dx=∫02011F(x)dx\int_{-2010}^{2011} F(x) dx - \int_0^{2010} F(x) dx = \int_0^{2011} F(x) dx
  3. C∫−20102011F(x)dx=0\int_{-2010}^{2011} F(x) dx = 0
  4. D∫−20102010(2F(−x)−F(x))dx=2∫02010F(x)dx\int_{-2010}^{2010} (2F(-x) - F(x)) dx = 2\int_0^{2010} F(x) dx

Correct answer

B. ∫−20102011F(x)dx−∫02010F(x)dx=∫02011F(x)dx\int_{-2010}^{2011} F(x) dx - \int_0^{2010} F(x) dx = \int_0^{2011} F(x) dx

Step-by-step solution

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