Day 46 in Mat120

• A new kind of function is a "net area" function, defined as an integral with a variable endpoint (e.g. the Fresnel integral).
• The variable of integration is a dummy variable (don't panic if we decide to change an x into a t for our own convenience).
• To solve most integrals, simply think of an anti-derivative (so much better than the nasty limit definition!).
• We require continuity of the integrand on the interval to use the fundamental theorem.
• The fundamental theorem "falls out" of the average rate of change. Hopefully it makes sense!

Today:

• 5.3 even solution endpoints

• No new worksheet.

• Return quizzes for section 5.3

• Quiz Opportunity over Section 5.4

• No problems to collect.

• Questions on old stuff?

• Section 5.4:
  • worksheet study questions

  • section summary

  • The total change theorem makes sense (using differentials).

  • Problems:
    • Section 5.3: #4, 23
    • Section 5.4: #2, 46, 53, 58

Next time: Substitution: the chain rule backwards (section 5.5.)