Indefinite Integration
Reduction Formulas for Trigonometric Functions
Grade 12
Question:
<p>If <span class="math">\(I_n = \int \cot^n x \, dx\)</span> (where <span class="math">\(u = \cot x\)</span>), then the value of <span class="math">\(I_2 + I_3 + I_4 + \ldots + I_9 + I_{10}\)</span> is <span class="math">\(l\)</span></p>
<p>(A) 1</p>
<p>(B) –1</p>
<p>(C) 2</p>
<p>(D) –2</p>
Step-by-Step Solution
Key Concept: Use the reduction formula for powers of cotangent and recognize telescoping in the sum
<p>This problem involves evaluating the sum of integrals using reduction formulas for <span class="math">$\cot^n x$</span>. The reduction formula and telescoping properties of the sum yield <span class="math">$l = -1$</span>.</p>
Correct Answer: B