Magnetic field Calculation of a Square Wire Loop (with a changed segment)

[Physicslearner500039]

Homework Statement

In Fig. 29-58, length a is 4.7 cm (short) and current i is 13 A. What are the (a) magnitude and (b) direction (into or out of the page) of the magnetic field at point P?

Relevant Equations

No equations from the problem

I tried to solve the above i have one confusion here.
I have marked the areas as shown

B2 = B4 = 0;
B1 , B5 Out of Page ; B3, B6 Into the Page.
B1 and B5 Calculation
Now main doubt is regarding the B field of the finite wire let us say 1. I took the derivation of the infinite wire as below from the textbook

Now instead of integrating from 0 to ∞ for 1, I integrated from 0 to 2a?

B1 = (μ *13)*[(2*a)/(2*√2*a)]/(2*π*2*a); Where R replaced with 2a
B1 = 19.5uT
Similarly for B5 = 19.5uT
Net field out B1 + B5 = 39.1uT
B3 and B6 Calculation
The same equation as above but integrated from 0 to a?
B3=B6 = (μ *13)*[a/√2*a]/(2*π*a); here i replaced R with a
B3=B6= 39.1; Net field into the paper B3+B6 = 78.2 uT

Hence the final field into the paper is = 78.2 - 39.1 = 39 uT;
I have doubts on the integrals of 0 to 2a and 0 to a is it correct? The answer is not matching it is 20uT and into the paper. Please advise.

 

[TSny]

For the infinite line you have

It might be better to rewrite this as $\large B = \frac {\mu_0 i}{4 \pi}\int_{-\infty}^{\infty} \frac{R ds}{(s^2+R^2)^{3/2}}$

How would this be modified for a finite length?