Indefinite Integration
Applications to Equations
Grade 12

Question:

<p>The number of solution(s) of the equation <span class="math">f(x) = x^3</span> in <span class="math">[0, 2\pi]</span> be:</p>
<p>(a) 0</p>
<p>(b) 3</p>
<p>(c) 2</p>
<p>(d) None of these</p>

Step-by-Step Solution

Key Concept: First determine <span class="math">f(x)</span> from the previous part, then count intersection points with <span class="math">y = x^3</span> on the given interval.
<p><strong>Solution:</strong> From Question 1, determine the explicit form of <span class="math">f(x)</span>. Then solve <span class="math">f(x) = x^3</span> graphically or algebraically in the interval <span class="math">[0, 2\pi]</span> by finding intersection points.</p>
Correct Answer: c

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