Not sure if you simply made a typo, but I get W=0.6209 instead of 0.06209. Also do you know what is the right answer, or just that yours is wrong?
Suppose that 2 Joules of work is needed to stretch a spring from its natural length of 35 cm to a length of 54 cm. How much work is needed to stretch it from 50 cm to 55 cm?
First change cm to m.
W = the integral from Xi to Xf of kx dx
so W=(1/2)k(Xf^2) - (1/2)k(Xi^2)
So solve for k
2=(1/2)(k(.54^2) - k(.35^2))
4=k(.1691)
k=23.6546
them solve for W with your new k value but with a different distance
W=(23.6546/2)(.55^2 - .50^2)
W=.620975 J
But the answer is wrong....
where is the length of stretch or compression in meters measured from the spring's natural length.
if the spring's natural length is 35 cm and the spring is stretched to a length of 54 cm , then ...
... use this value of to determine the spring constant, , then determine the work required to stretch the spring from 50 to 55 cm