$1.$ Know how to integrate using trigonometric substitution method $($section $7\mathrm{.}3).$ Show your setup by drawing the right triangle.$$

$2.$ Know how to integrate using partial fractions method $($section $7\mathrm{.}4).$

$3.$ Know how to integrate in general $($section $7\mathrm{.}5).$

$4.$ Know how to approximate a definite integral, size of error, and size of n using Trapezoidal Rule, Midpoint Rule, and Simpson Rule. $($section $7\mathrm{.}7)$ You will be given formula during the test.$$

$5.$ Know how to integrate improper integrals using limit$.($section $7\mathrm{.}8)$ Review L'Hospital Rule since you will use the rule often when you find limit$.$

$6.$ Know how to determine whether an improper integral using Comparison Theorem. $($section $7\mathrm{.}8)$ You need to compare using functions with $<,<=,>,>=.$ You are not allowed to use ~$($similar$)$ when you compare functions.$$

$7.$ Know how to find the arc length of a function. $($sec $8\mathrm{.}1)$

$8.$ Know how to find the surface area obtained by rotating a portion of a curve by a horizontal line $($y$=$a$)$ or a vertical line $($x $=$b$).$ Know how to express the integral in terms of x and in terms of y$.($sec $8\mathrm{.}2)$

$9.$ Know how to find c for a probability density function and how to find a probability using integration. $($sec $8\mathrm{.}5)$

$10.$ Know how to find the general solution y$=$f$($x$)$ for a differential equation. $($section $9\mathrm{.}3).$