[HP 50g] Vector integration

[FelipeACP]

I've been trying to evaluate a definite integral  of a vector, but I believe it is not possible given that the calculator always returns "Bad type argument". Is there any easy way to circumvent it or is there actualy a way to integrate a vector over a finite line?

For reference, the definite integral is:  4/4πε0 ∫(0.1ay-az) /[(.1^2+z^2)^(3/2)]dz from 0 to 0.05

Regards

[Maké]

Hi!, FelipeACP:

Write the integral, as ...

1: '4/(4*π*ε^0)*∫(0,1/20,1/10*(a*y-a*z)/((1/10^2+z^2)^(3/2), z)' 

Now, the result, with SOLVE, is ... π*a*(4.47214*y-1.05573)

[FelipeACP]

Hello Maké,

Thanks for the reply. I tried doing something similar but by 'ay' and 'az' I mean the unit vectors. Upon doing what you say, the z variable in 'az' is reckoned with when integrating with respect to z, which is not my intention. I want it just to be just a vector. In other words, I want essentially  to evaluate the integral of the array [0, 0.1, -1] / (0.1 + z^2)^3/2 with respect to z from 0 to 0.05. It should yield say 1.5ay+0.6az and display [0, 1.5,0.6] in HP. 

Whenever I try to integrate a vector with the longS function it returns "Bad argument type". The only solution I come up with was to integrate the unit vector ay and az separately, but this will be very tiresome later on. I was hoping there was any easier  workaround to this. 

[Maké]

Hi, FelipeACP:

See, in ... Wolfram Alpha ... 

Input:

Definite integral:

Result:

Visual representation of the integral:

In, the HP PRIME ...