It is said that you learn more from your mistakes than from your successes. This thought can be applied in both personal and academic sides. As for today, I am going to focus on my past midterm.

Question 1 (f) was for me a challenging question. The reason for this is that this question requires not only knowing how to apply integration techniques, but also , as one of my instructor would say, it requires being a little bit smart. Overall, this exercice requires to join and wisely use almost all techniques studied in class.

A reasonable first aproach would be to use substitution method with what it’s inside the square root. However, that wouldn’t have been an effective approach. Looking carefully t²+1 could be substitute by using trigonometry equivalences. t= tan(θ). With this substituion we will be left with ∫cos(θ)/sin²(θ) dθ. Now, another integration technique is necessary: substitution. This method can be very useful when knowing how to make a good substitution.

Tips for the final:

• Practice is the key. Intuition when evaluating integrals comes from practice. Not all integrals with similar forms can be solved similarly but after practice there are patterns that you start to notice.
• Trigonometric substituions. Practice when and how to use trigonometric substitutions, how to change the limits of the integral, how far should I go with my substituions, and when to stop and use a different method.