the first expression is the actual energy stored in the body.
the second expression is the enrgy stored in unit volume.

the factor 1/2 came becouz integration
here starts the proof
y-youngs modulus
L-initial length
F-FORCE REQUIRED
a-area of cros section
x-extension due to force
y=fL/ax
f=yax/ L
work done=f*dx
work={(yax) / (L) } dx
integrate from 0 to total extension.

substitute force=yax/L.

thus the answer

a person of ur calibre can do the integration.obtain the above answer.
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u ca do the integraton an