The integral

a

$$f$($x$)$ dx

is improper because the interval

$[$a$,$ $)$

is infinite. If f has an infinite discontinuity at a$,$ then the integral is improper for a second reason. In this case we evaluate the integral by expressing it as a sum of improper integrals of Type $2$ and Type $1$ as follows.

$$

a

$$f$($x$)$ dx $=$

ca

$$f$($x$)$ dx $+$

c

$$f$($x$)$ dx$,$ c $>$ a

Evaluate the following integral if it is convergent. $($If the quantity diverges, enter DIVERGES.$)$

$$

$0$

$$

$9$x$2$

$$dx