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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

Which of the following function(s) is/are even ?

Which of the following function(s) is/are even ?

Options

  1. Af(x)=∫0xln⁡(t+1+t2)dtf(x) = \int_0^x \ln(t + \sqrt{1 + t^2}) dt
  2. Bg(x)=∫0x(2t+1)t2t−1dtg(x) = \int_0^x \frac{(2^t + 1)t}{2^t - 1} dt
  3. Ch(x)=∫0x(1+t+t2−1−t+t2)dth(x) = \int_0^x (\sqrt{1 + t + t^2} - \sqrt{1 - t + t^2}) dt
  4. Dl(x)=∫0xln⁡(1−t1+t)dtl(x) = \int_0^x \ln \left( \frac{1 - t}{1 + t} \right) dt

Correct answer

A. f(x)=∫0xln⁡(t+1+t2)dtf(x) = \int_0^x \ln(t + \sqrt{1 + t^2}) dt

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