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You'll learnhow to turn a definite integral into arithmetic: find an antiderivative, substitute both limits, subtract — and why that last move is where the marks go.

A shaded region under a curve is worth a number, and that number turns out to be the distance between two heights on a completely different graph. Find an antiderivative, substitute both limits, subtract. The theorem is not where marks are lost — the subtraction is, and almost always when the lower value sits below the axis. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · FIND F, SUBSTITUTE, SUBTRACT — IN THAT ORDER · v2

the shaded area is F(b) − F(a), the gap between two heights

Before you start

What you're looking at

An integrand on top with its region shaded, and an antiderivative of it plotted underneath on the same horizontal scale.

The question

The shaded area is a number. Which two heights on the lower curve is it the distance between, and in what order?

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