Main Ideas

$\newcommand{\arraycolsep}[3]{} \newcommand{\dd}[2][]{\frac{d #1}{d #2}} \newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}} \newcommand{\veci}{\vec{\hat{\bf\imath}}} \newcommand{\vecj}{\vec{\hat{\bf\jmath}}} \newcommand{\utan}{\vec{\hat{t}}} \newcommand{\unormal}{\vec{\hat{n}}} \newenvironment{amatrix}[1]{% \begin{bmatrix} }{% \end{bmatrix} }$

$\newenvironment {prompt}{}{} \newcommand {\ungraded }[0]{} \newcommand {\HyperFirstAtBeginDocument }[0]{\AtBeginDocument }$

Here are the main points that will be addressed in the videos. Please read these and think about them as you watch.

An antiderivative of a function $f(x)$ is a function $F(x)$ whose derivative is $f(x)$ . In other words, the antiderivative of $f(x)$ , $F(x)$ , should satisfy $F'(x)=f(x)$ .
An antiderivative of $x^p$ is $\dfrac {x^{p+1}}{p+1}$ if $p \neq -1$ .
An antiderivative of $k$ , where $k$ is a constant, is $kx$ .
An antiderivative of $\dfrac {1}{x}$ is $\ln |x|$ .
An antiderivative of $\cos (x)$ is $\sin (x)$ .
An antiderivative of $\sin (x)$ is $-\cos (x)$ .
An antiderivative of $b^x$ is $\dfrac {b^x}{\ln (b)}$ .