<p>The area of the region bounded by \(y=\sqrt{1-x^2}\) and \(y=1-x\) in the first quadrant is: [MAU013]</p>
Step-by-Step Solution
Key Concept: y=\sqrt{1-x^2} is the unit circle (upper half). y=1-x is a line. They meet at (0,1) and (1,0). Area = (quarter circle area) - (triangle area) = \pi/4 - 1/2.
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<p>Both curves pass through \((0,1)\) and \((1,0)\).</p>
<p>Quarter circle area (from x=0 to x=1 under unit circle): \(\pi/4\).</p>
<p>Triangle area (under line \(y=1-x\) from x=0 to x=1): \(\frac{1}{2}\cdot1\cdot1=\frac{1}{2}\).</p>
<p>Since circle \(\ge\) line on \([0,1]\):</p>
<p>\[A=\frac{\pi}{4}-\frac{1}{2}\]</p>
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Correct Answer: B