Area Under the Curve
Area between polynomial curves
Grade 12
Question:
<p>The graphs of <i>f</i>(<i>x</i>) = <i>x</i>² and <i>g</i>(<i>x</i>) = <i>cx</i>³ (<i>c</i> > 0) intersect at the points (a, 0) & (1/c, 1/c²). If the region which lies between these & over the interval [0, 1/<i>c</i>] has the area equal to 2/3 then the value of <i>c</i> is</p>
<p>(A) 1</p>
<p>(B) 1/3</p>
<p>(C) 1/2</p>
<p>(D) 2</p>
Step-by-Step Solution
Key Concept: Set up the integral of |x² – cx³| from 0 to 1/c and equate it to 2/3, then solve for c.
<p>Not provided in source text</p>
Correct Answer: A