## Calculus: Early Transcendentals (2nd Edition)

(a) $$A(2)=2\cdot6=12.$$ (b) $$A(6)=6\cdot6=36.$$ (c) $$A(x)=x\cdot6=6x.$$
(a) Here we just get the rectangle bounded by $y=6$, $y=0$ (the $t$ axis), $t=0$ (the $y$ axis) and $t=2$. So the sides of this rectangle are $a=6$ (height) and $b=2$ (width) so the area is $$A(2)=2\cdot6=12.$$ (b) Here we just get the rectangle bounded by $y=6$, $y=0$ (the $t$ axis), $t=0$ (the $y$ axis) and $t=6$. So the sides of this rectangle are $a=6$ (height) and $b=6$ (width) so the area is $$A(6)=6\cdot6=36.$$ (c) Here we just get the rectangle bounded by $y=6$, $y=0$ (the $t$ axis), $t=0$ (the $y$ axis) and $t=x$. So the sides of this rectangle are $a=6$ (height) and $b=x$ (width) so the area is $$A(x)=x\cdot6=6x.$$