Area Under the Curve
Area bounded by curves
Grade 12
Question:
<p>A function <i>y</i> = <i>f</i>(<i>x</i>) satisfies the differential equation <i>dy/dx</i> – <i>y</i> = cos <i>x</i> – sin <i>x</i>, with initial condition that <i>y</i> is bounded when <i>x</i> → ∞. The area enclosed by <i>y</i> = <i>f</i>(<i>x</i>), <i>y</i> = cos <i>x</i> and the y-axis in the 1st quadrant is</p>
<p>(A) √2 – 1</p>
<p>(B) √2</p>
<p>(C) 1</p>
<p>(D) 1/2</p>
Step-by-Step Solution
Key Concept: Solve the linear differential equation with the boundedness condition, then compute the area between f(x) and cos x using integration.
<p>Not provided in source text</p>
Correct Answer: A