CPM Homework Help : APCALC Problem 11-33

Examine the integrals below. Consider the multiple tools available for integrating and use the best strategy for each part. Evaluate each integral and briefly describe your method.

$\int _ { 2 } ^ { 6 } \frac { 1 } { \sqrt { x - 2 } } d x$
Step 1(a):
$=\lim\limits_{a\to 2}\int_a^6(x-2)^{-1/2}dx$

$\int \ln(x)dx$
Hint (b):
Use integration by parts. Let $f = \ln(x)$ and $dg = dx$ .

$\int _ { 3 } ^ { t ^ { 2 } } \frac { d } { d x } ( \frac { x } { x - 2 } ) d x$
Hint (c):
This is the integral of a derivative, so use the Fundamental Theorem of Calculus.