The area of the closed igure bounded by $x = - 1,\;x = 2$ and $y = \left\{ {\begin{array}{*{20}{c}} { - {x^2} + 2\;,\;x \le 1}\\ {2x - 1\;\;,\;\;x > 1} \end{array}} \right.$ and the $x$-axis is

$\frac{{16}}{3}\,{\rm{sq unit}}$

$\frac{{10}}{3}\,{\rm{sq unit}}$

$\frac{{13}}{3}\,{\rm{sq unit}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The area of the closed igure bounded by

x = - 1,\;x = 2

and

y = \left\{ {\begin{array}{cccccccccccccccccccc} { - {x^2} + 2\;,\;x \le 1}\\ {2x - 1\;\;,\;\;x > 1} \end{array}} \right.

and the

x

-axis is

View answer and explanation

Correct option: A

\frac{{16}}{3}\,\mathrm{sq unit}

Option A (

\frac{{16}}{3}\,\mathrm{sq unit}

) is correct because it represents the definite integral of the piecewise function over the given interval.

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