Task $2$: Triple Integral $-$ Cartesian Coordinates

Given a solid bounded region by the surface $\backslash ($ z$=1-$x$^\{2\}\backslash )$ and the planes $\backslash ($ z$=1-$y$,$ y$=1\backslash )$ and $\backslash ($ x$=0\backslash ).$

a$)$ Draw the diagram using mathematical application $($GeoGebra etc.$)$

$(3$ marks$)$

b$)$ Draw the projection of diagram using mathematical application $($GeoGebra etc.$)$

from:

i$.\backslash ($ x $\backslash )-$axis

$(3$ marks$)$

ii$.\backslash ($ y $\backslash )-$axis

$(3$ marks$)$

iii. z$-$axis

$(3$ marks$)$

c$)$ Hence, find the volume of the integral from each projection.

i$.\backslash ($ x $\backslash )-$axis

$(7$ marks$)$

ii$.\backslash ($ y $\backslash )-$axis

$(7$ marks$)$

iii. $\backslash ($ z $\backslash )-$axis

$(7$ marks$)$