please solve using castiglianos theorum, if you do not I will dislike, I am looking for integrals, not a formula. please answer all $4$ questions thank you

possible answer list: $1\mathrm{.}387,\mathrm{.}5194,\mathrm{.}16044,\mathrm{.}41933,\mathrm{.}00001375,\mathrm{.}00257,\mathrm{.}0186,\mathrm{.}00139,1\mathrm{.}489,\mathrm{.}3411,\mathrm{.}1,\mathrm{.}00411$

using Castigliano$$s theorem, determine the deflection of point B in the direction of the force F for the steel bar shown. The Young$$s modulus E $=30$x$106$ lb$/$in$2$ and the modulus of rigidity G $=11\mathrm{.}5$x$106$ lb$/$in$2.$ Neglect contributions due to transverse shear. Match the following below. Numbers are all in inches.

Group of answer choices

Deflection due to bending in AB

$[$ Choose $]1\mathrm{.}3870\mathrm{.}51940\mathrm{.}160440\mathrm{.}419330\mathrm{.}000013750\mathrm{.}002570\mathrm{.}01860\mathrm{.}001391\mathrm{.}4890\mathrm{.}34110\mathrm{.}10\mathrm{.}00411$

Deformation due to axial loading

$[$ Choose $]1\mathrm{.}3870\mathrm{.}51940\mathrm{.}160440\mathrm{.}419330\mathrm{.}000013750\mathrm{.}002570\mathrm{.}01860\mathrm{.}001391\mathrm{.}4890\mathrm{.}34110\mathrm{.}10\mathrm{.}00411$

Deflection due to torsion

$[$ Choose $]1\mathrm{.}3870\mathrm{.}51940\mathrm{.}160440\mathrm{.}419330\mathrm{.}000013750\mathrm{.}002570\mathrm{.}01860\mathrm{.}001391\mathrm{.}4890\mathrm{.}34110\mathrm{.}10\mathrm{.}00411$

Deflection due to bending in OA

$[$ Choose $]1\mathrm{.}3870\mathrm{.}51940\mathrm{.}160440\mathrm{.}419330\mathrm{.}000013750\mathrm{.}002570\mathrm{.}01860\mathrm{.}001391\mathrm{.}4890\mathrm{.}34110\mathrm{.}10\mathrm{.}00411$