Let $\displaystyle g(x)=\frac{\sin^2(x)}{x^2}.$

(a) Use a calculator or computer algebra system to evaluate $\displaystyle \int_{1}^{\,t} {g(x)}\, dx$ for $t$ = 2, 5, 10, 100, 1000, and 10000. Make sure each answer is correct to five decimal places.

$t$ = 2:

$t$ = 5:

$t$ = 10:

$t$ = 100:

$t$ = 1000:

$t$ = 10000:

(b) Use the Comparison Theorem to determine whether $\displaystyle \int_{1}^{\,\infty} {g(x)}\, dx$ is convergent or divergent.

? Convergent Divergent  1. $\displaystyle \int_{1}^{\,\infty} {g(x)}\, dx$