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
\(\frac{1}{3}sq\hspace{1 mm}units\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(y = x(2-x) \Rightarrow y= 2x - x^{2}\);
\(\int^{2}_{0}(2x-x^{2} = (x^{2}-\frac{x{3}}{3})^{2}\)
solving further gives (4 - \(\frac{1}{3} * 8) - (0) = \frac{4}{3} sq\hspace{1 mm}unit\)
Source: Myschool Past Questions Archive (Record #539)