Mathematics (AS)·Integration · NSSCAS 1.9.2
Definite & improper integrals
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In this lesson you will learn to evaluate a definite integral by integrating, then substituting the top and bottom limits and subtracting. You will use the square-bracket notation and see exactly why the plus c is not needed. You will work full examples with whole-number and rational powers. Then you will take the AS step up into improper integrals and see how some areas are finite even when the graph runs to infinity or blows up near an edge.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.9.2):
- Evaluate definite integrals using the square-bracket notation, substituting both limits and subtracting.
- Evaluate simple improper integrals, such as the integral from 0 to 1 of x to the power minus a half, and the integral from 2 to infinity of x to the power minus two.
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