When I want to emphasize a noun by italicizing, do I need to italicize the article of the noun or not? For example, is this correct?
"Is it an apple?"
"No, it is an orange."
Or, is this correct?
"Is it an apple?"
"No, it is an orange."
A similar question for the.
It is called the curse of dimensionality.
Or
It is called the curse of dimensionality.
Because italicizing for emphasis can select any word as well as parts of words, italicizing an article means that you are emphasizing that article for some purpose. Compare:
"Is it a orange?"
"No, it is an orange." (An emphasized in contrast to "a.")
"Is it an apple?"
"No, it is an orange." (Orange emphasized in contrast to "apple.")
Stylistically, it is better to omit italics if they aren't necessary for a given purpose, since emphasis is watered down with frequent use. That is one reason why both MLA and APA recommend minimizing the use of italics for emphasis, and why more colloquial guides recommend against overuse ("but don't overwork this device"). So there's no strict rule that demands you include the article, and an expectation that you have a deliberate reason for italicizing something. The rest is your decision.
As a general guide, consider how you would say the sentence out loud. If you emphasise both the article and the other word(s), then put the article in italics:
"No, it is an orange."
If (as would be more common) you instead find that you say the article with a normal voice but put extra emphasis on the following word(s), then don't put the article in italics:
"No, it is an orange."
This general guide applies to just about any situation where you would say a particular word or words louder (see: that's an example) to indicate emphasis (there's another!). It's particularly useful in more conversational writing where you're trying to capture or replicate the non-verbal signals that spoken language includes, but as TaliesinMerlin's answer notes, don't overdo it in more formal writing.
