The area (in sq.

Question

The area (in sq. units) of the region

{ (x, y) : 0 $$ \le $$ y $$ \le $$ x2 + 1, 0 $$ \le $$ y $$ \le $$ x + 1,

$${1 \over 2}$$ $$ \le $$ x $$ \le $$ 2 } is :

Accepted Answer

$$A = \int\limits_{{1 \over 2}}^1 {({x^2} + 1)dx + } $$ $\int\limits_1^2 {} $${(x + 1)dx}$

= $${\left[ {{{{x^3}} \over 3} + x} \right]_{{1 \over 2}}^1 + \left[ {{{{x^2}} \over 2} + x} \right]_1^2}$$

$${ = \left( {{4 \over 3} - {{13} \over {24}}} \right) + \left( {4 - {3 \over 2}} \right)}$$

$${ = {{19} \over {24}} + {5 \over 2}}$$

$${ = {{79} \over {24}}}$$

Solutions · 1