Example problem 1: Find the area between the curves y = x and y = x2 between x = 0 and x = 1. Step 1: Find the definite integral for each equation over the range x = 0 and x = 1, using the usual integration rules to integrate each term. (see: calculating definite integrals)...
$\begingroup$ @robjohn: OK fair enough, I wasn't really trying to define sine and cosine so much as I was trying to point out that radians are usually introduced via the arclength of a wedge, not the area of a wedge (divided by 2). Also, I didn't have a problem with using that...
Riemann sums use the method of 'slicing' the area of a graph to isolate the equation used to calculate definite integrals. Follow example problems of using Riemann sums to find an area even when divided into different sections. Create an account Table of Contents When to Use a Riemann Sum...
The most important reason for finding the generating function for a sequence is thatfunctionshave a much larger “toolbox” to work with. For example, you can’t findderivativesandintegralsof sequences, but you can apply those procedures to functions. Not all sequences have generating sequences....
To find out why all her apple pies crumbled. To a tightrope walker named Zekund The a due to gravity beckoned. His performance was great At about 9.8 Meters per second per second. Consider the pitiful plight Of a runner who wasn’t too bright. ...
It’s worth realizing that his whole paper is less than 3 pages long, and right before his conclusions we’re seeing triple integrals: So what is (3) about? It’s presumably something like a Second-Law-implies-heat-death-of-the-universe statement (but what’s thi...
How can one prove the statement $$\lim_{x\to 0}\frac{\sin x}x=1$$ without using the Taylor series of $\sin$, $\cos$ and $\tan$? Best would be a geometrical solution. This is homework. In my math class, we are about to prove that $\sin$ is continuous. We found out, ...