Learning Objectives

More formulas:

$\int \sec^{2} x d x = \tan x + C$

$\int \csc^{2} x d x = - \cot x + C$

$\int \sec x \tan x d x = \sec x + C$

$\int \csc x \cot x d x = - \csc x + C$

$\int \frac{1}{\sqrt{1 - x^{2}}} d x = \sin^{- 1} x + C$

$\int \frac{1}{1 + x^{2}} d x = \tan^{- 1} x + C$

$F (b) = F (a) + \int_{a}^{b} F^{'} (x) d x$

or $\int_{a}^{b} F^{'} (x) d x = F (b) - F (a)$

Example: Given a velocity function $v (t) = 3 t - 5$ (in meters per second) for a particle in motion.

a. find the net displacement of the particle over the time interval [0, 3]

b. Find the total distance travel of the particle over the time interval [0, 3]

Even function: $f (- x) = f (x)$ , symmetric with respect to y-axis.

Odd function: $f (- x) = - f (x)$ , symmetric with respect to origin.

For continuous even functions, $\int_{- a}^{a} f (x) d x = 2 \int_{0}^{a} f (x) d x$

For continuous odd functions, $\int_{- a}^{a} f (x) d x = 0$

Instructions

5.4. Integration Formulas and the Net Change Theorem.pdf (PDF file)

5.4: 207-215, 221-229 odd

Participate Chapter 5 Discussion for questions and answers.
Keep notes for main concepts, problems you struggled with and your reflection etc.
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