Topics: (may be updated when I have time)
• Antiderivatives problem #18 on WeBWorK
• Definite integrals and the Fundamental Theorem of Calculus
Note: there are two different things which have very similar notations, even though they are not the same type of object at all. They are:
The indefinite integral: this represents the set of all of the antiderivatives of the function. (Recall that an antiderivative of is a function whose derivative is ). The indefinite integral is a function containing an arbitrary, undetermined constant (the constant of integration).
Notation for the indefinite integral:
A definite integral: this represents a signed area or a sum of signed areas, the areas between the graph of &latex f(x)$ and the x-axis, between two bounds. A definite integral is generally a number.
Notation for a definite integral:
Even though these two things are unrelated to begin with, the Fundamental Theorem of Calculus (part II) comes in to tell us that we can evaluate a definite integral by using antiderivatives, so the same type notation is used for both things!
[This is like the fact that represents two different things: it is the quotient when 2 is divided by 5, and it is also the amount we get when we cut a unit length into 5 pieces and take 2 of them. It happens that the second thing is the answer to the first division problem, so we can use the same notation and usually don’t worry about it!]
Here are some videos from Khan Academy:
• Make sure that you have done everything from the first day post.
• Review finding definite integrals and the Fundamental Theorem of Calculus.
• Finish the WeBWorK on Antiderivatives and do the new assignments on the Fundamental Theorem of Calculus – due by Tuesday 11 PM, but don’t wait to the last minute!
• There will be a quiz at the start of class next time. Be on time! It will be on finding antiderivatives (and solving differential equations)
• Monday is a holiday. Happy Labor Day! Next class is next Wednesday, the 6th of September.
Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question.