Dual Enrollment Program DE Course: Math 1540 Integral Calculus
Math 1540 covers integrals of algebraic, exponential, logarithmic, and trigonometric functions, with applications.
This is an LSU Integrative Learning Core (ILC) course that awards general education credit. Math 1530 and Math 1540 together cover the material of LSU Math 1550. LSU credit will not be given for this course and Math 1431, Math 1550, or Math 1551.
Note: Math 1540 is designed for students who already have credit in Math 1530. Students will need only one MyLab Math access code for this sequence.
Topics and Objectives
Section numbers refer to Calculus: Early Transcendentals, 3e (Briggs, Cochran, Gillett, Schultz).
4.2 Mean Value Theorem
- Apply properties of Rolle's Theorem and the Mean Value Theorem
- Find points guaranteed to exist by Rolle's Theorem
- Find points guaranteed to exist by the Mean Value Theorem
- Solve applications using the Mean Value Theorem
4.5 Optimization Problems
- Apply properties of optimization problems and objective functions
- Solve optimization problems involving geometry, number operations, and conic sections
- Solve applications by optimizing functions
4.6 Linear Approximations and Differentials
- Write a linear approximation and estimate the value of a function
- Graph a function and its linear approximation to identify underestimates and overestimates
- Use linear approximations to estimate a quantity
- Use linear approximations to estimate changes in a given variable
- Write a differential expression the change in y as a function of the change in x
4.7 L'Hopital's Rule
- Evaluate limits of the form 0/0
- Evaluate limits of the form infinity/infinity, 0*infinity, or infinity-infinity
- Evaluate limits of the form 1^infinity, 0^0, or infinity^0
- Evaluate limits using the appropriate method
4.8 Newton’s Method
- Given an initial approximation, use Newton’s method to find the first two approximations
- Use Newton's method to find solutions to equations
4.9 Antiderivatives
- Find general antiderivatives and indefinite integrals
- Find particular antiderivatives and solve initial value problems
- Relate solutions to initial value problems to their graphs
- Solve applications involving antiderivatives
- Find the equation of a curve given information about the derivative
- Solve initial value problems
5.1 Approximating Areas under Curves
- Apply properties of Riemann sums
- Approximate displacement over an interval given a velocity function
- Evaluate left, right, and midpoint Riemann sums
- Evaluate Riemann sums from tables
- Use sigma notation and evaluate expressions in sigma notation
- Solve applications using the area under a curve
5.2 Definite Integrals
- Apply properties of net area and definite integrals
- Approximate net area given functions
- Express Riemann sums as definite integrals
- Evaluate definite integrals using geometry
- Approximate net area from graphs
- Use properties of definite integrals
- Evaluate definite integrals using Riemann sums
5.3 Fundamental Theorem of Calculus
- Apply properties of the Fundamental Theorem of Calculus
- Evaluate area functions
- Evaluate definite integrals using the Fundamental Theorem of Calculus
- Find areas bounded by functions
- Evaluate derivatives of definite integrals
- Work with area functions and graphs of area functions
5.4 Working with Integrals
- Use symmetry to evaluate definite integrals
- Find average values of functions over given intervals
- Use the Mean Value Theorem for Integrals
- Find average values of functions
5.5 Substitution Rule
- Verify formulas using differentiation
- Apply properties of composite functions and the Substitution Rule
- Find indefinite integrals using a given
- Use a change of variables to find indefinite integrals
- Use a change of variables to evaluate definite integrals
- Find general antiderivatives and indefinite integrals
- Find areas of regions using integration that requires substitution
- Evaluate definite integrals using the Fundamental Theorem of Calculus
- Find particular antiderivatives and solve initial value problems
- Find average values of functions over given intervals
6.1 Velocity and Net Change
- Apply properties of velocity and net change
- Determine displacement and position from velocity
- Find position and velocity from acceleration
- Solve applications involving net change and future value
6.2 Regions Between Curves
- Apply concepts associated with the area between two curves
- Find the area between two curves
- Rewrite areas by changing the variable of integration
6.3 Volumes by Slicing
- Apply concepts associated with finding volumes by slicing
- Use the general slicing method to find volumes of solids
- Use the disk method to find volumes of solids
- Use the washer method to find volumes of solids
- Find volumes of solids using an appropriate method
- Compare volumes of solids
6.4 Volume by Shells
- Use the shell method to find volumes of solids generated by revolving a region about the y-axis
- Use the shell method to find volumes of solids generated by revolving a region about the x-axis
- Use the shell method to find volumes of solids
- Find volumes of solids using an appropriate method
6.5 Length of Curves
- Find arc lengths by integrating with respect to x
- Solve applications involving arc length
6.7 Density and Mass
- Apply concepts associated with mass, work, and force
- Find the mass of thin bars with given density functions
- Solve applications involving work
- Solve applications involving force
Syllabus & Pacing Guide
| Name | Last Modified |
|---|---|
| S26 Math 1540 DE Syllabus [docx] | 2025-12-10 |
| S26 Math 1540 DE Pacing Guide [docx] | 2026-01-04 |
Course Profile
| Name | Last Modified |
|---|---|
| Math 1540 Integral Calculus COURSE PROFILE 9-27-2023 [docx] | 2025-12-10 |
Class Notes
| Name | Last Modified |
|---|---|
| 4.2 Mean Value Theorem [docx] | 2019-07-12 |
| 4.5 Optimization Problems [docx] | 2019-07-12 |
| 4.6 Linear Approximations and Differentials [docx] | 2019-07-12 |
| 4.7 L'Hôpital's Rule [docx] | 2019-07-12 |
| 4.8 Newton's Method [docx] | 2019-07-12 |
| 4.9 Antiderivatives [docx] | 2019-07-12 |
| 5.1 Approximating Areas under Curves [docx] | 2019-07-12 |
| 5.2 Definite Integrals [docx] | 2019-07-12 |
| 5.3 Fundamental Theorem of Calculus [docx] | 2019-07-12 |
| 5.4 Working with Integrals [docx] | 2019-07-12 |
| 5.5 Substitution Rule [docx] | 2019-07-12 |
| 6.1 Velocity and Net Change [docx] | 2019-07-12 |
| 6.2 Regions Between Curves [docx] | 2019-07-12 |
| 6.3 Volume by Slicing [docx] | 2019-07-12 |
| 6.4 Volume by Shells [docx] | 2025-04-08 |
| 6.5 Length of Curves [docx] | 2019-07-12 |
| 6.7 Physical Applications [docx] | 2019-07-12 |