The integral
I=∫xcosxdx
can be approached by deciding which factor will be differentiated and which will be antidifferentiated.
Two students propose the following strategies.
• Strategy A: Differentiate x and antidifferentiate cosx.
• Strategy B: Differentiate cosx and antidifferentiate x.
(a) For each strategy, write the first term that would be produced after carrying out the indicated differentiation and antidifferentiation. (A complete evaluation of I is _not_ required for this part.)
(b) Discuss which strategy is more efficient for finishing the evaluation of I. In your explanation, compare the complexity of the remaining integral in each case and justify your conclusion.