Items tagged with calculus


I would like to have my calculus results in its simplified form; below are some of the scenarios that can explain this.



As you can see the results are much simplified and in reduced form compared to what Maple gives. This has been tested for all integrals with roots and integrals with trigonometry functions. Is there any workaround in Maple that I would use to get it like the textbook result.



I am not able to understand why Maple fails to compute and display the integrals for Eqn (1) and Eqn (8). I have a integral table to cross-verify the integrals for each of these in here


Also, another integral I am trying to calculate in MWE2 (attached file) in which the integral computed doesn't make any sense.


int(sqrt(x^3.(ax+b)), x)

int((x^3.(ax+b))^(1/2), x)





int(7*x^3+3*x^2+5*x, x)



int(1, x)



int(1/(x^2+1), x)



int(1/(ax^2+bx+c), x)



int(x^n, x)



int(sqrt(x(ax+b)), x)

int(x(ax+b)^(1/2), x)





How can I plot a paraboloid?


I can't get Simpson's Rule to work properly in Maple for f(x)=cos(e^-x)

According to Wolfram Alpha, I should be getting something like -0.5. Clearly that's not what I'm getting. Please help?

> f := proc (x) options operator, arrow; cos(6*exp(-x)) end proc;
x -> cos(6 exp(-x))

S := evalf(int(f(x), x = 0 .. 1));
S1 := evalf((1/6)*(1+0)*(f(0)+4*f(1)+f(2)));
S2 := evalf((1/12)*(1+0)*(f(0)+4*f(1)+2*f(2)+4*f(3)+f(4)));


Hi all,

How to calculate this integral:

for k>0,m>0

Int(exp(-(1/2)*v/k)*v^3*exp((1/2)*v/m)*Ei(1, -(1000*I)*v+(1/2)*v/m), v = 0 .. infinity)

I'm  tried to take advantage of with(IntegrationTools) but I failed

and and I got a strange result ,like this:

Dear Maple experts,


I would like to teach volume of solids generated by revolution of an area between two curves by washers & cylindrical shell methods uisng Maple technology to my students. In this regard, I request the Maple experts to provide easy commands to meet my requirement.


With thanks & best regards.



Associate Professor in Mathematics

First Question: How to define nx1 matrix Y:=(y1,y2,...,yn) ? (n is a Natural number while it is ungiven)

Second Question: How to derivative of matrix Y with respect to nx1 matrix X:=(x1,x2,...,xn) ?


My efforts for the first question:  (I know to define 6x1 matrix etc. , but I dont know to define nx1 matrix

restart: Matrix(1..6,1,symbol=y) 


My efforts for the second question:

restart; with(VectorCalculus);
Matrix([x^2, x*y, x*z]);
Jacobian([x^2, x*y, x*z], [x, y, z]);

Can you help me? 

how i

Find the length of the curve in interval of x

equation 1 : xi+1=xi− (f·gy−fy·g)/(fx ·gy −fy ·gx)
equation 2: yi+1=yi− (fx·g−f·gx)/(fx·gy-fy·gx)

My quesiton are, deriving equations (1) and (2) above and constructing a single Maple function called newt2d that implements both of these recurrence relation.

I apolgize in advance if I don't write my question correctly.  This is my first time posting a question. 

A string is wound symmetrically around a circular rod. The string goes exactly
4 times around the rod. The circumference of the rod is 4 cm and its length is 12 cm.
Find the length of the string.
Show all your work.

(It was presented at a meeting of the European Mathematical Society in 2001,
"Reference levels in mathematics in Europe at age16").

Can you solve it? You may want to try before seing the solution.
[I sometimes train olympiad students at my university, so I like such problems].

eq:= 2/Pi*cos(t), 2/Pi*sin(t), 3/2/Pi*t; # The equations of the helix, t in 0 .. 8*Pi:
p:=plots[spacecurve]([eq, t=0..8*Pi],scaling=constrained,color=red, thickness=5, axes=none):
plots:-display(plottools:-cylinder([0,0,0], 2/Pi, 12, style=surface, color=yellow),
                         p, scaling=constrained,axes=none);

VectorCalculus:-ArcLength(<eq>, t=0..8*Pi);



Let's look at the first loop around the rod.
If we develop the corresponding 1/4 of the cylinder, it results a rectangle  whose sides are 4 and 12/4 = 3.
The diagonal is 5 (ask Pythagora why), so the length of the string is 4*5 = 20.


diff(F(x,F(x)), x);


how to differentiate this?


(D[1](F))(x, F(x))+(D[2](F))(x, F(x))*(diff(F(x), x))


how to find (D[1](F))(x, F(x)) and (D[2](F))(x, F(x)) ?


i guess need define new calculus for two variables

Limit((F(x+h,F(x+h)) - F(x,F(x)))/h, h = 0);

Limit((F(x+h,F(x)) - F(x,F(x)))/h, h = 0);
Limit((F(x,F(x+h)) - F(x,F(x)))/h, h = 0);

Limit((F(x+h,F(x,y)) - F(x,F(x,y)))/h, h = 0);
Limit((F(x,F(x+h,y)) - F(x,F(x,y)))/h, h = 0);


if inside F(x) is F(x,y)

it seems need to find the basic definition of F(x,y) first

if i define F(x,y) as

F := (x,y) -> min(x,y)/max(x,y);


i may be wrong, how to differentiate correctly?

A new Maple e-book, Multivariate Calculus Study Guide, is now available. Part of the Clickable Calculus collection of interactive Maple e-books, this guide takes full advantage of Maple’s Clickable Math approach. It has over 600 worked examples, the vast majority of which are solved using interactive, Clickable Math techniques. 

Deisgned to help students taking this course, instructors may also find this e-book useful as a guide to using Clickable Math to teach Multivariate Calculus.

See Multivariate Calculus Study Guide for more information.



and why are there decimal points after certain numbers?

I'm taking 2nd semester calculus and in this maple lab, I can't seem to get Maple to evaluate this correctly. Any help is appreciated.

My friend did this and got the first constant, 392..., and just a2, so it was 392.07a2

I am doing a Calculus assignment and I can't find the commands for certain things.

1.Given the function f(x) = ((x+1)^2) / (1+x^2)

i) The domain of continuity of f(x)

ii) The intervals of increase and decrease of f(x) by using test points.


2. Use the IVT to prove existence of a root to the equation x^3 +10x^2 -100x +50=0 in the interval [-20,10]. Use again the IVT to show that there is a 1st root in [-17,-15], a 2nd toot in [0,1] and a 3rd root in [ 5,6]. Find or approximate those roots with Maple. (the bolded is what I need help).

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