What Splits, and What Does Not

You'll learnhow to rearrange a definite integral without evaluating it, and which two rearrangements look like the rest and are not rules at all.

A short list of rules lets you move a definite integral around before you evaluate anything. Sums and constant multiples come apart, products and quotients never do, cutting a region at a point is free, and turning the direction of travel round costs a minus sign. Every rule here is one picture: a region, a direction, and a number. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · WHAT SPLITS, WHAT DOES NOT, AND WHAT THE SIGN RECORDS · v2

a region, a direction of travel, and a number you can rearrange

Before you start

What you're looking at

A curve with the region under it shaded — yellow where it adds, violet where it subtracts.

The question

Which rearrangements of that integral are allowed, and which two are not rules at all?

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