The recipe is quite simple to understand looking at an example (and it is understood best by having paper and pencil to follow it):
f:= x -> x^2 the parabola with its inverse g:= y -> sqrt(y).
Say you want the integral of g over 0 ... 2, which (here) is the area between the graph and its horizontal axis.
That is the same as the area of the rectangle minus the area between the graph of g and the vertical axis, where the rectangle has corners 0, 2 and g(0)= f^(-1)(0) and g(2)= f^(-1)(2).
Now recall the geometric interpretation of the compositional inverse of a function: it is reflection at the diagonal.

Basically, I am considering buying Maple 11 as I am a college student hwo will soon be taking college-level math courses. But I am weak in these old areas of mathematics, the stuff you explore in high school. I want to know if Maple 11 will serve the majority of my math needs as a student, whether it is pre-algebra, algebra, geometry, calculus, etc.

Have you ever plotted a function in Maple and then found that the range you plotted it on wasn't really what you wanted? You can always re-execute the command, of course, but that means working out exactly what the range is for that interesting feature you want to investigate, and if you've made changes to the plot those will be lost. However Maple has the ability to zoom in on a plot interactively, without re-executing the command.
The Axis Properties dialog lets you change the range numerically, but you can also do so using the mouse. Go to the plot toolbar and click on the **Scale plot axes** button (it looks like a red ball with an arrow). If you have an animation you will need to click on the word "plot" above the toolbar to switch from animation to plot toolbar. Now put the mouse in the middle of the plot and drag it. Dragging it down will zoom out, increasing the range; dragging it up will zoom in. The **Translate plot axes** button lets you 'pan' i.e. move the centre of the axis ranges without changing the range size.

My

previous blog entry was a real success.
Even though my original idea about multi-part MIME has not gotten anywhere, I do now have a concise way to package a maplet with supplemental files in a single package that can be downloaded via the WWW and automatically extracted and executed.
Most of the ideas were presented by acer.
acer first suggested that I look at the interactive interface to the InstallerBuilder. The idea here was to embed the maplet in a worksheet saved in a help database (hdb).
This did work, but was not suitable for actual use due to the overhead of the installer. In the attempt to reduce this overhead, acer then supplied some code that used march and LibraryTools.
To test the product of this interaction, download the file at the URL

http://www.math.sc.edu/~meade/TEST/SimpleTest.mla.

I got an interesting question about integration yesterday. The question was about the integral of the rather innocuous looking function f := sqrt(1+sin(x)). The inside of the square root is always non-negative so the function is continuous (and bounded!) so it must have a continuous integral.
The question I was asked, was if the following result was a bug in Maple:
Int(sqrt(1+sin(x)),x) = (2*(sin(x)-1))*sqrt(1+sin(x))/cos(x)
since the right-hand side is definitely not continuous at x=-Pi/2 + 2*n*Pi!

My apologies if this has been posted before, but a quick search didn't turn it up. I'd like to have a simple, "clickable" way, preferably in the "PlotBuilder", to shade in the region *between* two 2D curves or two 3D surfaces. I know that there are packages to do this, but I'd like my students to be able to do it without learning any new commands or loading any new packages --- it's just too useful when you are teaching calculus.
Thanks for listening!
----Josh

So I am taking multi variable calculus this semester and we have been asked to use maple to complete an assignment. I have never used maple before so I tried to read the tutorial we were given. Anyway, it was written by some incompetent fool as I am now more confused than when I started. The concepts are appallingly illustrated and I have no idea what to do. I have attempted to do most questions and I will probably get part marks for most, but I am completely clueless regarding this one.
The Question is as follows: "Determine the distance from the plane 2x + y - z = 1 to the plane 2x + y - z = 6"

So I am taking multi variable calculus this semester and we have been asked to use maple to complete an assignment. I have never used maple before so I tried to read the tutorial we were given. Anyway, it was written by some incompetent fool as I am now more confused than when I started. The concepts are appallingly illustrated and I have no idea what to do. I have attempted to do most questions and I will probably get part marks for most, but I am completely clueless regarding this one.
The Question is as follows: "Determine the distance from the plane 2x + y - z = 1 to the plane 2x + y - z = 6"

... I doubt that there has ever been a better way to learn the relationship between numbers - and even mathematics in general - than the slide-rule from days-gone-by, and the ability to plot functions using modern computer technology. For the young people here who may not have ever used a slide rule, below is a link to a virtual slide rule: virtual slide rule

I wish, and think...

Consider a sum:
Sum((-1)^(i+1)*Sum(1/j,j=1..i)*x^i,i=1..infinity);
value(%);
The result given by Maple 11 is:
sum((-1)^(i+1)*(Psi(i+1)+gamma)*x^i, i = 1 .. infinity)
However, from an calculus book I know the answer is:
log(1+x)/(1+x).
How can I get this result from Maple? Whether should I give some assumptions?
Best wishes.

Hello:
I just bought this maple sofware last week, and I need some help with that. I am tryingto do my homework from college, "calculus and trig" I need to know how I can erase after I have bee done an exercise in the little window going to: maple 11, untitle, tools, tutor, single variable?
I this is very good but I jsut can not erase anyting after I did an exercise , please I need help!! thank you!

Unless calculus has changed, when evaluating a definite integral, i.e., one with limits, first one performs the integration on the expression and then one evaluates the result for the upper limit and subtracts the result evaluated for the lower limit. That of course means that the indefinite integral (without limits) has to be produced before evaluating the result using the limits. Considering that, here is the confusing situation I have run into. Maple returns an answer, complicated to be sure, but an answer to
int(sin(x)*sin(x^3+x), x = 0 .. infinity)
suggesting that it CAN integrate sin(x)*sin(x^3+x)

i have a project due in my calculus class on simple harmonic motion. i have to imput the equation of s=8cos((sqrt(2)/5)*pi*t) into maple, which i can do but then i am asked to solve the equation when t is equal to 0. now i know the answer is 8 but i have no idea to make maple do that using the equation already typed in. in addition to this, i then need to differentiate the s function in order to find v and a. i am also having a hard time doing this. if anyone knows how to put these in so they will work that would be a big help.

I am a high school math teacher with a subject degree. I have enrolled in a Calculus on the computer class and the course requirements required me to get maple 10. I was excited to get it. As I went through my calculus classes I don't believe maple was around. Anyway, the math of the subject is extremely easy as it should be. The hardest thing is getting the syntax of the commands. Remembering to put the ; at the end and stuff like that but im trudging through.
The reason for this email is this. I am highly considering Maple 11 in the fact that it allows text and stuff on the plots. So with this in mind I am also not seeing the way that I can learn this program well enough to make it useful in my classroom. I would absolutely love to use it for my classroom. I just don't see how to make it look good with the combination text and math in the worksheet view or even getting the document view going. I am a real newbie to this program and want to do so much more with this program. Is there anything that you'll can suggest?

Another pesky student question.
Is the speed of light an asymptotic, or limiting value that no other body can perfectly attain ?
Does light travel at exactly this value or very very close to it?
Would it make sense to try to exactly attain the value of c with something other than EM energy, or would our attempts be similar to taking a limit like in simple calculus ?
v/r,