Critical Thinking
This question is from the AP Calculus textbook, in the Integrals section.
In regards to the Core Competency Profiles, I believe that I fit the profile of Profile 5, “I can evaluate and use well-chosen evidence to develop interpretations; identify alternatives, perspectives, and implications; and make judgments. I can examine and adjust my thinking.” To solve this question, I first used my knowledge of the power rule for integration to integrate the expression. Next, I plugged numbers in – but I realized that the Euler’s number in the expression made it complicated and I didn’t know what to do. Considering alternate approaches, I tried leaving the expression as it was, but that wasn’t the fully simplified answer. Next, I sought feedback from my peers, which unfortunately didn’t help. Lastly, I went to Ms. Eaton to ask for help, and realized that I could have raised the exponent to create ln4 instead of 2ln2. Taking this experience and feedback into account will help me solve future integrals with e in them.