Find the area under the curve y=12x3\displaystyle {y}=\frac{{1}}{{{2}{x}^{{3}}}} from x=1\displaystyle {x}={1} to x=t\displaystyle {x}={t} and evaluate it for t=10,t=100\displaystyle {t}={10},{t}={100}. Then find the total area under this curve for x1\displaystyle {x}\geq{1}.
(a) t = 10
 



(b) t = 100
 



(c) Total area