My book said that the cis isomer has a higher melting point. But I dont understand isn't that the trans isomer can pack more efficiently, because the trans isomer less bulky/ create less 'kink' than the cis isomer?
Between Trans and Cis isomer Cis has the boiling point as it's µ ≠ 0 ,Both of the isomers have exactly the same atoms joined up in exactly the same order. That means that the Van der Waals dispersion forces (London Forces) between the molecules will be identical in both cases. The difference between the two is that the Cis isomer is a polar molecule whereas the trans isomer is non-polar.And since Trans form is symmetric along CH₃ molecule, the main thing to check is polarity hence boiling point is compared.
If I understand correctly, part of the issue stems from your question referring to the cis/trans isomers differently from what's shown in the image. In the answer to 17(a,b) the book identifies X as the trans isomer, but your question appears to describe X as being the cis isomer with higher boiling point.
I took a look in Scifinder but it doesn't seem like there is isomer-specific experimental thermal data for the two compounds. I would argue that a "packability" judgement is pretty difficult to make with this pair of isomers because of their low symmetry and the minimal difference between isomers.
Some of this ambiguity may be due to the use of cis and trans, rather than the preferred E/Z. Some people may refer to C/C=C(C)/CCC(=O)O (a SMILES string) as the cis isomer because the two methyl groups are cis, whereas others refer to C/C=C(C)\CCC(=O)O as the cis isomer because the two highest (and two lowest) priority groups via the CIP system are cis. Can this be clarified.