Definite Integration
Trigonometric Integrals
Grade 12
Question:
<p>The integral <span class="math">\int_{\pi/3}^{\pi/6} 3\tan^7 3x \cdot \sin^2 3x (2\sec^2 x \cdot \sin^2 3x + 3\tan x \cdot \sin^6 x) dx</span> is equal to</p>
<p>(a) <span class="math">-\frac{1}{9}</span></p>
<p>(b) <span class="math">\frac{7}{18}</span></p>
<p>(c) <span class="math">-\frac{1}{18}</span></p>
<p>(d) <span class="math">\frac{9}{2}</span></p>
Step-by-Step Solution
Key Concept: Use trigonometric identities and substitution to reduce the integrand to a simpler form that can be integrated directly.
<p>This is a definite integral requiring substitution and simplification techniques. The integrand involves powers of trigonometric functions that can be reduced using identities.</p>
Correct Answer: C