https://imgur.com/a/wtvpRHh
So that's a link to a question I'm stuck on. I tried using first principles instead of using the shortcut, since the shortcut isn't that intuitive for me. I can understand and calculate the pure endowment part, but for the term insurance this is what I did:

tP45=1-(t/58) and to find the force of mortality between 45 and 65, I took 20P45=.65517=e^(20ux). Then solved for ux as .02114. Then I integrated between 0 and 20 for (1-(t/58))*.02114*(e^.06t), or tP45*ux*v^t.

I ended up with an answer of .28037 for the 20 term insurance, while the solution has .200806. Can someone provide clarity on what I did wrong or why my approach may not work? Thank you in advance!