max125

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These are questions asked by max125

integral.mw

I am trying to evaluate any which way the integral:

int(exp(-(sqrt(4*x^2+4*y^2+4*z^2)^3)), z = -sqrt(4-x^2-y^2).. sqrt(4-x^2-y^2),y=-sqrt(4-x^2)..sqrt(4-x^2),x=-2..2);

The program just hangs, so i click on 'stop current operation'.

Then I tried:

evalf(Int(exp(-(sqrt(4*x^2+4*y^2+4*z^2)^3)), z = -sqrt(4-x^2-y^2).. sqrt(4-x^2-y^2),y=-sqrt(4-x^2)..sqrt(4-x^2),x=-2..2));

It returns the integral back unevaluated.

It's true that I could use a change of variables, changing to spherical coordinates would be best here. But I would like to know if I did set up the original Cartesian integral correctly. Is there some workaround I can apply to get a numeric answer. I am satisfied with a decimal approximation. Then I can compare to the change of variable result. An exact answer would be even better of course.

Maple gives me the incorrect answer to the hundredth place. (arithmetic.mw)

>15000*(1+.06/365)^(10*365)
>                        27330.47804

I tried using an exact fraction 15000*(1+(6/100)/365)^(10*365) as well.

For some reason the Maple software is not evaluating the last bounds for a triple integral.

But the evalf command works.

I am writing a small code to find median and mean. The code works for an even number of terms, not for an odd number of terms. I tried to find the error but cannot.

restart:medianmean:= proc(x) local a,b,c,d,m,g;
a:=sort(x); b:=nops(x); c:=nops(x)/2; d:=(nops(x)+1)/2;
m:=(a[c]+a[c+1])/2; g:=add(a)/b;
if (b mod 2 = 0) then evalf([a,m,g]) ;
else evalf([a,a[d],g]);
end if; end proc:

 

I am not sure why I am getting this RootOf result when I solve for x.

Here is my code.

restart:
eq:=4*x^2+2*y(x)^2=32.5625:
deq:=solve(  diff(eq,x), diff(y(x),x) ):
deq=3;
y(x)=solve(deq=3,y(x));
x=solve(deq=3,x);

The last equation we are solving is  -2x / y = 3.
So we should get y  = -2/3 x and  x = -3/2 y.

The Maple software correctly solves for y in terms of x,
but gives an odd Rootof answer when solving for x. Why is that?

I am not sure how to intepret RootOf(2*_Z+3*y(_Z)).

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