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CSS Applied Mathematics QUESTION #1327
Question 1
The exact value of \(\int_1^3\dfrac{1}{x^2}\,dx\) is:
  • \(\dfrac{1}{3}\)
  • \(\dfrac{2}{3}\)✔️
  • \(\dfrac{1}{9}\)
  • \(\dfrac{4}{3}\)
Correct Answer Explanation
\(\int_1^3\dfrac{1}{x^2}\,dx=\left[-\dfrac{1}{x}\right]_1^3=-\dfrac{1}{3}+1=\dfrac{2}{3}\). This is the exact value; the Trapezoidal Rule approximation approaches this as the step size decreases.