Q76 / 150 · MHT CET 2016 · Mathematics

The area of the region bounded by the curve $y = 2 x - x^{2}$ and $x -$ axis is

A
$\frac{2}{3} s q u n i t s$
Correct answer
B
$\frac{4}{3} s q u n i t s$
C
$\frac{5}{3} s q u n i t s$
D
$\frac{8}{3} s q u n i t s$

Solution

A = \int_{0}^{2} (2 x - x^{2}) d x

\Rightarrow A = {[x^{2} - \frac{x^{3}}{3}]}_{0}^{2}

\Rightarrow A = [4 - \frac{8}{3}]

\Rightarrow A = \frac{4}{3} s q u n i t s

Hence, the correct answer is option: 'B'.

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