Integral (with respect to d(z/σ))

[MechEng2010]

Hello all,

I have uploaded a .gif of the integral. The limits are just values, as I know what d,h, and σ₁ are. d and h are the lower and upper limits defined for the probability distribution function and σ₁ is the standard deviation.

I have not seen this type of integral before, I am not sure how I can evaluate this numerically as I need to do this with respect to d(z/σ))?

This is on a research paper I am currently reviewing, Can anyone help?

Thanks.

 

[Simon Bridge]

why not substitute $u=z/\sigma_1$ ?

 

[MechEng2010]

Would that help me to integrate this between the numerical limits of d/σ1 and h/σ1? Sorry still confused, could you explain further. Thanks.

 

[Simon Bridge]

If that's what you want to do.
Of course you'd have to substitute for the limits as well.

if you integrate from z=a to z=b but you make the the substitution in the integrand that u=f(z) then what happens to your limits?

But - if u = z/s, what is dz/du ? what is d(z/s)/du ? Put du = ... for each. Compare.