Definite Integration
Integration of Determinants
Grade 12
Question:
<p>Let <span>\(f(x) = \begin{vmatrix} 2\cos 2x & \sin 2x & -\sin x \\ \sin 2x & 2\sin 2x & \cos x \\ \sin x & -\cos x & 0 \end{vmatrix}\)</span>, the value of <span>\(\int_0^{\pi/2} \{f(x) + f'(x)\} dx\)</span> is</p>
<p>(a) π/2</p>
<p>(b) π</p>
<p>(c) 3π/2</p>
<p>(d) 2π</p>
Step-by-Step Solution
Key Concept: Split the integral and use integration by parts or recognize that <span>$\int f'(x)dx = f(x)$</span>, then evaluate at the bounds.
<p>Use the property that <span>$\int_0^{\pi/2} \{f(x) + f'(x)\} dx = [f(x)]_0^{\pi/2} + \int_0^{\pi/2} f(x) dx$</span>. Evaluate the determinant and compute the integral.</p>
Correct Answer: B