The area of the region enclosed by [y 4 x^2, x^2 9 y] and [y 4], is equal to :

Question

The area of the region enclosed by $$y \leq 4 x^{2}, x^{2} \leq 9 y$$ and $$y \leq 4$$, is equal to :

Accepted Answer

$$y \le 4{x^2},\,{x^2} \le 9y,\,y \le 4$$

So, required area

$$A = 2\int_0^4 {\left( {3\sqrt y  - {1 \over 2}\sqrt y } \right)dy} $$

$$ = 2\,.\,{5 \over 2}\,\,\,\,\,\,\,\,\left[ {{2 \over 3}{y^{{3 \over 2}}}} \right]_0^4$$

$$ = {{10} \over 3}\,\,\,\,\,\,\,\,\,\,\left[ {{4^{{3 \over 2}}} - 0} \right] = {{80} \over 3}$$

Solutions · 1