Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.
- 4 sq units
- 2 sq units
-
\(\frac{4}{3}sq\hspace{1 mm}units\)
- \(\frac{1}{3}sq\hspace{1 mm}units\)
The correct answer is: C
Explanation
\(y = x(2-x) \Rightarrow y= 2x - x^{2};\int^{2}_{0}(2x-x^{2} = (x^{2}-\frac{x{3}}{3})^{2}\\
solving further gives (4 - \frac{1}{3} * 8) - (0) = \frac{4}{3} sq\hspace{1 mm}unit\)