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Question: Three Questions: Function defined by derivative, function define d by Integral,

Question:Three Questions: Function defined by derivative, function define d by Integral,

Maqroll 25 Maple 2023
integration programming differentiation operator
June 16 2023
2

First Question

 

Let's define a function:

f := proc (x) options operator, arrow; a*x/(4*x^2+b) end proc

proc (x) options operator, arrow; a*x/(4*x^2+b) end proc

(1.1)

now define a new function that is the derivative of f.

g := proc (x) options operator, arrow; diff(f(x), x) end proc

proc (x) options operator, arrow; diff(f(x), x) end proc

(1.2)

g is not what I expected. I expect:

g := proc (x) options operator, arrow; a/(4*x^2+b)-8*a*x^2/(4*x^2+b)^2 end proc

NULL

and if i try to calculate g(0), the result is:

g(0)

Error, (in g) invalid input: diff received 0, which is not valid for its 2nd argument

 

NULL

instead of

a/b

a/b

(1.3)

Second Question

 

I need to define an integral function in which the variable is an integration boundary:

 

h := proc (x) options operator, arrow; int(f(t), t = 0 .. x) end proc

proc (x) options operator, arrow; int(f(t), t = 0 .. x) end proc

(2.1)

if I try to calculate :

h(x)

int(a*t/(4*t^2+b), t = 0 .. x)

(2.2)

how can i do the calculation and display the explicit form of the function, and assign to a name ?

  (1/8)*a*ln(4*x^2+b)-(1/8)*a*ln(b)

(1/8)*a*ln(4*x^2+b)-(1/8)*ln(b)*a

(2.3)

Third Question

 

is there a way to write a system of equation in text mode (or math) in the usual math notation with a big curly bracket followed by the list of equation ? graphically similar to the piecewice operator that seems to be not useful for this purpose?

About the first and the second question i read on the web something but i don't understand deeply what is the reason of the behaviour. I would like to understand really that. Thanks a lot.

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