Definite Integration
Grade 12
Question:
<p>The area bounded by the x-axis and the part of graph of y = cos x between x = <span class="math-tex">\(\frac{-\pi}{2}\)</span> and x = <span class="math-tex">\(\frac{\pi}{2}\)</span> is separated into two regions by the line x = k. If the area of the region for <span class="math-tex">\(\frac{-\pi}{2} \leq x \leq k\)</span> is three times the area of the region for <span class="math-tex">\(k \leq x \leq \frac{\pi}{2}\)</span>, then k is equal to :</p>
<p style="display:inline"><span class="math-tex">\(\frac{\pi}{3}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{\pi}{6}\)</span></p>
<p style="display:inline">arc sin <span class="math-tex">\(\left(\frac{1}{3}\right)\)</span></p>
<p style="display:inline">arc sin <span class="math-tex">\(\left(\frac{1}{4}\right)\)</span></p>
Step-by-Step Solution
Key Concept: Equate the definite integral of the function from the lower limit to k with three times the definite integral from k to the upper limit to solve for the boundary value.
<p><span class="math-tex">$\frac{\pi}{6}$</span></p>
Correct Answer: B