If f(x) is an improper rational function like (x² + 1)/(x² - 5x + 6), what is the first step in integration?
If f(x) is an improper rational function like (x² + 1)/(x² - 5x + 6), what is the first step in integration?
- A. Divide numerator by denominator
- B. Directly use partial fractions
- C. Substitute x = tan θ
- D. Integrate numerator and denominator separately
Answer: A) Divide numerator by denominator
Explanation: For improper rational functions (degree of numerator ≥ denominator), we must perform long division to express it as a polynomial plus a proper rational function.
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