(a) Find the exact area under the curve $f(x)=1/x^{1.1}$ from $x = 1$ to $x = t$ for $t$ = 10, 100, $10^4,$ $10^6,$ $10^{10},$ and $10^{20}.$ Make sure your answers are correct to five decimal places.

$t$ = 10:

$t$ = 100:

$t$ = $10^4:$

$t$ = $10^6:$

$t$ = $10^{10}:$

$t$ = $10^{20}:$

(b) Find the exact area under the curve $f(x)=1/x^{1.1}$ for $x \ge 1.$ If the area is infinite, type "infinity" in lower-case letters for your answer.

Total area =

(c) Repeat (a) for the function $g(x)=1/x^{0.9}.$

$t$ = 10:

$t$ = 100:

$t$ = $10^4:$

$t$ = $10^6:$

$t$ = $10^{10}:$

$t$ = $10^{20}:$

(d) Find the exact area under the curve $f(x)=1/x^{0.9}$ for $x \ge 1.$ If the area is infinite, type "infinity" in lower-case letters for your answer.

Total area =