Contents of this Calculus 1 tutorial:

Integration rules, Constant multiplier, Integrating sums, Integrating products, Integrating a fractions, Integrating composite functions.

Text of slideshow

Integration is a much more entertaining activity than differentiation.

For example, here is a product:

Differentiation is very simple: we only have to remember one rule, and then we can use it for any kind of product.

But if we have to integrate, well, the situation is a lot more exciting.

There will be at least five different rules, and we will have to be able to figure out which method is needed for a given case.

A tiny change is enough to require a different method.

So, we won't get bored.

In order to overcome these minor difficulties, we group the integration rules so that we start from the simplest rule, and progress towards the more difficult ones.

Let's see the rules.

INTEGRATION RULES

The first rule is exactly like the one for differentiation. A constant multiplier can be factored out.

The second rule is about integrating sums. This one is also similar to differentiation: parts of a sum are integrated separately.

The rule for products is more exciting. Because there is no such rule.

If we have to integrate a product, we have several choices. Exactly five.

But we will have to know which rule to use, and it is not recommended to decide by tossing a coin.

Luckily, there will be a separate slideshow for each method that will reveal how to use that particular rule and when to use it.

Fractions will be a similar story. There will be a few methods for integrating fractions. Let's see, maybe three?

And composite functions also have at least two methods.

So we better get to work.

Integration rules, Constant multiplier, Integrating sums, Integrating products, Integrating a fractions, Integrating composite functions.

 

Integration rules

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Integration rules, Constant multiplier, Integrating sums, Integrating products, Integrating a fractions, Integrating composite functions.

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