Indefinite Integration
Integration of Irrational Functions
Grade 12
Question:
<p>Find <span>\(\int \frac{dx}{(x-p)\sqrt{(x-p)(x-q)}}\)</span></p>
<p>(A) <span>\(\frac{2}{p-q}\sqrt{\frac{x-p}{x-q}} + c\)</span></p>
<p>(B) <span>\(-\frac{2}{p-q}\sqrt{\frac{x-q}{x-p}} + c\)</span></p>
<p>(C) <span>\(\sqrt{(x-p)(x-q)} + c\)</span></p>
<p>(D) None of these</p>
Step-by-Step Solution
Key Concept: Use substitution to convert the integrand with square roots into a simpler rational or trigonometric form.
<p><strong>Step 1:</strong> Use the substitution to rationalize the expression.<br/><strong>Step 2:</strong> Simplify to a standard form.<br/><strong>Step 3:</strong> Integrate to obtain the result.</p>
Correct Answer: A