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}sqhspace{1 mm}units) -
D.
(frac{1}{3}sqhspace{1 mm}units)
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} sqhspace{1 mm}unit)