My student had difficulty showing that 3 < A < 3.75 and I was stuck for a couple of seconds too. Reason? The question did not state clearly how many rectangles are required. The answer is 2 rectangles, but if a student used 3 or more rectangles or 2 rectangles that are different from what the setter has in mind, then they would probably not get the values 3 and 3.75.
The setter did not consider enough when setting this question.
My student was trying out the following question that requires integration by parts:
where she chose . The reason was she interprets “1” as which is under “A” of the LIATE method. Since “A” is before “T”, she chose to differentiate one instead and got stuck.
This is one reason why the topic of techniques of integration, especially by parts, requires some foresight. One should consider what happens to the working upon his / her choice for “u”. This example shows us that we should not learn techniques of integration by memorising formulas blindly.