QJEEM17Ma2b29: JEE Main 2017 Mathematics - Class 12 JEEM17Ma2b29 Solution: The area (in sq. units) of the region is

Question

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The area (in sq. units) of the region

\left\{ {\left( {x,y} \right):x \ge 0,x + y \le 3,{x^2} \le 4y\,and\,y \le 1 + \sqrt x } \right\}

is

Accepted Answer

Area of shaded region

=

\int\limits_0^1 {\left( {1 + \sqrt x } \right)dx} + \int\limits_1^2 {\left( {3 - x} \right)dx} - \int\limits_0^2 {{{{x^2}} \over 4}dx}

=

\left[ x \right]_0^1 + \left[ {{{{x^{{3 \over 2}}}} \over {{3 \over 2}}}} \right]_0^1

+

3\left[ x \right]_1^2 - \left[ {{{{x^2}} \over 2}} \right]_1^2 - \left[ {{{{x^3}} \over {12}}} \right]_0^2

=

{5 \over 2}

sq. unit

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