The area of the region S=(x,y):y^28x, y√2,x, x1 is:

Question

The area of the region $S=\{(x,y):y^2\le8x,\ y\ge\sqrt2\,x,\ x\ge1\}$ is:

Accepted Answer

Required area

$$ = \int\limits_1^4 {\left( {\sqrt {8x}  - \sqrt 2 x} \right)dx} $$

$$ = \left. {{{2\sqrt 8 } \over 3}{x^{{3 \over 2}}} - {{{x^2}} \over {\sqrt 2 }}} \right|_1^4$$

$$ = {{16\sqrt 3 } \over 3} - {{16} \over {\sqrt 2 }} - {{2\sqrt 8 } \over 3} + {1 \over {\sqrt 2 }}$$

$$ = {{11\sqrt 2 } \over 6}$$ sq. units

Solutions · 1