How to master integration and differentiation?

Solution 1:

First of all, if you're struggling with derivatives, you've got almost three strikes against you when it comes to knowing how to integrate! So focus first on getting very familiar with derivatives. Then integration follows much more easily.

For both taking derivatives and integrating, Paul's Online Math Notes are an excellent source for tutorials, practice problems, and "cheat sheets". I've linked you to the notes involving derivatives. You can review just about everything covered in Calculus I, II, and III, all at the same site, by navigating the tabs and the menu on the left of the webpages.

For quick guides ("cheat sheets"), Paul's Notes provides links here to pdf documents that you can download to your own computer for reviewing "off-line."

For your convenience, I'll include links to the study sheet on derivatives, and the study sheet on integrals.

IMPORTANT:

Apart from that, but more importantly, if you want to master taking derivatives of functions, and integration, you'll need to devote yourself to practice, and lots of it. Mathematics is not a spectator sport. To develop competence and mastery, you need to do math, and not just "read about it."

Solution 2:

Khan Academy has a brilliant playlist for calculus which covers everything from epsilon-delta limit to chain rules and definite and indefinite integrals. Also you might want to check out this article at acko.net to get a tangible feel for limits.

Solution 3:

One of the best ways to improve on differentiation and integration is to do tons of problems. It is very important to focus on differentiation before you start integration. A strong understanding of differentiation makes integration more natural. I recommend looking at James Stewart's Calculus textbook. It has hundreds of differentiation and integration problems. If you need help and want to see solved problems step-by-step, then Schaum's Outlines Calculus is a great book that is inexpensive with hundreds of differentiation and integration problems. The more problems you solve the easier it becomes.

Solution 4:

I you want to improve in derivaties and integrals at the same time, you can write any function and calcule its derivaty. Then you try to return to the original... integrating.