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Find the area bounded by the curve y = x(2-x). The x-axis, x = 0...

Mathematics
JAMB 1999

Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.
  • A. 4 sq units
  • B. 2 sq units
  • C. \(\frac{4}{3}sq\hspace{1 mm}units\)
  • D. \(\frac{1}{3}sq\hspace{1 mm}units\)
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Correct Answer: Option C
Explanation
\(y = x(2-x) \Rightarrow y= 2x - x^{2};

\int^{2}_{0}(2x-x^{2} = (x^{2}-\frac{x{3}}{3})^{2}\\
solving further gives (4 - \frac{1}{3} * 8) - (0) = \frac{4}{3} sq\hspace{1 mm}unit\)

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