(a) Find the exact area under the curve $y=1/x^3$ from $x = 1$ to $x = t$ for $t$ = 10, 100, and 1000.

$t$ = 10:

$t$ = 100:

$t$ = 1000:

(b) Find the total area under the curve $y=1/x^3$ for $x \ge 1.$ If the area is infinite, type "infinity" in lower-case letters for your answer.

Total area =