# How to prepare for Integral Calculus (Calculus 2)

I'm majoring in computer engineering and I have Calculus 2 coming up this semester. From what I understand, Calculus 2 is the most difficult math class in the engineering path.

Over the summer, I've been studying the material to be covered in Calculus 2 and I'm not sure which area should be given the most focus - based purely upon degree of difficulty. I was able to pass Calculus 1 with an A so I'm hoping that the degree of difficulty is just hype.

Here are the topics my book covers for Calculus 2:

• Applications of Integration
• Techniques of Integration
• Further Applications of Integration
• Differential Equations
• Parametric Equations and Polar Coordinates
• Infinite Sequence and Series

I've been focusing heavily on Techniques of Integration, and it seems that this section is the 'heart' of the class. I've covered and practiced through half of Further Applications of Integration and haven't had too much trouble.

Is this a good strategy to prepare for this course?

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I suspect Further applications... covers volumes of revolution solids? From experience, I would say this is a topic that students often struggle with. This and your last topic, Infinite sequences and series. However, if you haven't had any trouble so far, I would say you shouldn't worry too much about this course. – M Turgeon Aug 6 '13 at 22:02
@MTurgeon Thank you for the comment! Applications of Integration covered volumes and revolution solids. I thought that part was fun! Further Applications has as topics: Arc Length, Area of Surface of Revolution, Applications to Physics and Engineering, Applications to Economics and Biology, and Probability. – free_mind Aug 6 '13 at 22:05
@code4me since you are interested, you might look at my calculus II course website from last time I taught. Odds of you doing more than I do computationally are somewhat slim at American universities. I also have oodles of solutions and stuff posted. Enjoy supermath.info/CalculusII.html – James S. Cook Aug 7 '13 at 1:50
@JamesS.Cook in your experience, which section is the most difficult for students? – free_mind Aug 7 '13 at 11:31
@code4me it depends on the student. Calculus II really has great diversity in topics. The typical engineering school calculus is something like 25% integration, 25% basic ODEs, 25% sequences and series, 25% applications to volumes/work etc... each of these topics will appeal more strongly to differing populations so it's hard to say what is most troubling unless I know you better. Statistically speaking, it's easy: series and sequences kill most because they require logic and calculation as opposed to mainly calculation. My main advice, make time to study. – James S. Cook Aug 7 '13 at 13:03

I would say to master the basics. Make sure you know all of the elementary antiderivatives. Focusing on techniques of integration is a good idea, as knowing which method of integration to use is harder than knowing which differentiation rule to use (in my opinion anyway). Judging from your strong foundations in differential calculus, you should be fine.

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I haven't used these in Calc 1, but they will be used in Calc 2, I've had to brush up on these since it's been a while:

logarithms, & inverse trigonometric functions

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