0 years, 84 days

## Dot product with time derivative variabl...

Maple

I try to dot product 2 vector that contain time derivative

the answer should be v . u_rho = rhodot

but Maple doesn't give me a proper answer. What should i do?

kind regard

restart;

with(LinearAlgebra);

with(Typesetting);
Settings(typesetprime = true);
Settings(typesetdot = true);

v := <diff(rho(t), t)*cos(theta(t)) - rho(t)*diff(theta(t), t)*sin(theta(t)), diff(rho(t), t)*sin(theta(t)) + rho(t)*diff(theta(t), t)*cos(theta(t)), diff(z(t), t)>

u_rho := <cos(theta(t)), sin(theta(t)), 0>

v . u_rho

## Triple integral doesn't work...

Maple 2024

I try to solve triple integraton in Maple with this code.

r := a + (b - a)*z/h;
x1 := sqrt(r^2 - y^2);
V := int(int(int(1, x = -x1 .. x1), y = -r .. r), z = 0 .. h);

but it leaves the last integral dz in the answer and warns: unable to determine if a*h/(-b+a) is between 0 and h; try to use assumptions or use the AllSolutions option
What is the problem?
and i need to get V = Pi*h(a^2 + ab +b^2)/3

Regards

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