Indefinite Integration
Integration with Exponential Functions
Grade 12
Question:
<p>If <span>\(\int (e^{2x} + 2e^x \cos x - e^{-x}(e^x + e^{-x})) dx = g(x)e^{(e^x + e^{-x})} + c\)</span>, where <span>\(c\)</span> is a constant of integration, then <span>\(g(0)\)</span> is equal to</p>
<p>(a) 2</p>
<p>(b) <span>\(e^2\)</span></p>
<p>(c) <span>\(e\)</span></p>
<p>(d) 1</p>
Step-by-Step Solution
Key Concept: Simplify the integrand and use substitution to match the given form of the antiderivative
<p>Evaluate the integral and find the function <span>$g(x)$</span>, then substitute <span>$x = 0$</span>.</p>
Correct Answer: D