Area Under the Curve
Area between two curves
Grade 12
Question:
<p>If area bounded by the line <i>y</i> = <i>x</i>, curve <i>y</i> = <i>f</i>(<i>x</i>) and lines <i>x</i> = 1, <i>x</i> = <i>t</i>, is <i>t/2</i>(2<i>t</i> – 1 + 1/<i>t</i> + <i>t</i>) then <i>f</i>(<i>x</i>) =</p>
<p>(A) 3/2 + 4/(x+1)</p>
<p>(B) 3/4 + x/(x–1)</p>
<p>(C) (x+1)/(x–1)</p>
<p>(D) Not provided</p>
Step-by-Step Solution
Key Concept: Differentiate the given area formula with respect to t to find f(t), then replace t with x to get f(x).
<p>Not provided in source text</p>
Correct Answer: A