<p>Calculate <span>\(A_1 + A_2 = \int_0^{\pi/2} \cos x \, dx\)</span>.</p>
Step-by-Step Solution
Key Concept: Recognize that the antiderivative of cosine is sine, then apply the Fundamental Theorem of Calculus with the given limits.
<p><strong>Step 1:</strong> Evaluate the definite integral: <span>$\int_0^{\pi/2} \cos x \, dx = \sin x \Big|_0^{\pi/2}$</span></p><p><strong>Step 2:</strong> Apply limits: <span>$\sin\left(\frac{\pi}{2}\right) - \sin(0) = 1 - 0 = 1$</span></p><p>∴ Answer is <span>$A_1 + A_2 = 1$</span>.</p>
Correct Answer: 1