Evaluate the improper integral integral from 1 to infinity of 1 / (x^2 + 1) dx.
Answer and explanation
Correct answer: B. pi/4
- Step 1: The anti-derivative of 1/(x^2 + 1) is arctan(x). Step 2. Evaluate: lim_{t->inf} [arctan(t) - arctan(1)] = pi/2 - pi/4 = pi/4. Answer: pi/4. Why not the others: arctan approaches pi/2 as x tends to infinity.
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