As for this midterm, the relatively difficult question for me was number 3. This question was not hard, but I was confused by the function inside the integral. Although I knew the fundamental theorem of calculus was the key to solve this, I did not substitute root t before using the theorem. I thought in the wrong way at the beginning and hardly came back. The formula of FTC would help if I were writing down.
Tips to remember:
- Do not overthink.
Start a question from what you could do. Sometimes rearrange the equation would make it clear. To avoid overthinking, come back to the problem later and try another method.
2. Think of the method or theorem behind the question.
Before answering the question, identify what theorem can be used. Write down the formula of the theorem besides the equation, and then compare.
Before solving an integral, think of all rules that may be helpful based on its characteristics. For instance, to get rid of square root, use u-substitution and square u.
- Do not skip steps.