Practice question · Multiple choice
Substitution requires changing the limits too when working with a definite integral. What goes wrong if you keep the original ones?
Hints
- With u = x², integrating x from 0 to 2 means u runs from where to where?
- Ask what the limits are limits OF once the variable has changed.
Show the answer
B. You would evaluate at the old variable's limits, which belong to x
Why
Limits are values of the variable, so changing the variable changes them: x from 0 to 2 becomes u from 0 to 4. Option 2 names the legitimate alternative, substitute back and keep the old limits, and the error is doing neither, which mixes u's function with x's endpoints.
Practise Integration by Substitution
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