Practice question · Put in order
Order the steps for evaluating a definite integral with Part 2 of the Fundamental Theorem.
- Evaluate F at the upper limit b
- Find any one antiderivative F of the integrand
- Subtract to obtain F(b) - F(a)
- Evaluate F at the lower limit a
- Check that the integrand is continuous on the interval from a to b
Hints
- The theorem has a hypothesis before it has a recipe.
- Both endpoint values must exist before the subtraction can happen.
Show the answer
- Check that the integrand is continuous on the interval from a to b
- Find any one antiderivative F of the integrand
- Evaluate F at the upper limit b
- Evaluate F at the lower limit a
- Subtract to obtain F(b) - F(a)
Why
Continuity licenses the theorem; then any antiderivative will do, because the + C cancels in the subtraction. That last fact is why the recipe never asks you which antiderivative to pick.
Practise The Fundamental Theorem of Calculus
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