Today we will do example problems involving definite integrals. We will use the Fundamental Theorem of Calculus, the Mean Value Theorem for Integrals, and the Average Value of a function.

We will go over the assigned problems in section 4.3, We will discuss the Fundamental Theorem of Calculus, The Mean Value theory for integrals, the Second Fundamental Theorem of Calculus and the average value of a function.

We will review the estimating of areas using Riemann Sums, the midpoint method, and the trapezoidal method. We will use the limit as the number of rectangles used for our estimates approaches infinity to find the exact area. The definite integral is the exact area. We will do a few example problems.

We will use the limit of a sum to define the definite integral. We will define the term Riemann Sum, you can use it to find values for definite integrals. The theory is important as it is leading up to the Fundamental Theorem of Calculus which equates the definite integral to the area between a continuous curve and the x-axis.

We will find areas on a graph using upper and lower sums, left and right sums, and using the midpoint rule. We will review sigma notation. We will evaluate definite integrals.

School closed for hurricane Milton.

School closed for hurricane Milton.

We will discuss the assigned problems on page 287-9. Antiderivatives are emphasized in these problems so they will be a good review of the process. We will begin the study of area as it relates to integrals.

We will do problem examples from pages 287-9 in the textbook. This will give us a variety of integral examples and also some application problems.

We will begin our study of integrals by finding general solutions for antiderivatives. We will work toward finding particular solutions and then to evaluating integrals.