This course examines integral calculus topics. Students are presented with integration techniques for functions of one variable and more applications of definite integrals. Students explore numerical techniques of integration. Students also examine the area function, Riemann sums, and indefinite integrals, and apply these to real-life problems. The course concludes with the Fundamental Theorem of Calculus.
This undergraduate course is 7 weeks.
This course has a prerequisite. Please see details in the Prerequisite section below.
Attendance and participation are mandatory in all university courses, and specific requirements may differ by course. If attendance requirements are not met, a student may be removed from the course. Please review the Course Attendance Policy, Tuition Refund Policy and all University Policies in the Catalog for more information.
Topics and Objectives
Introduction to Integration
- Estimate the area under a curve with finite sums.
- Estimate the area under a curve with geometric formulas for area.
- Interpret sigma notation and associated algebra rules.
- Perform Riemann sums over given intervals.
- Calculate definite integrals.
- Calculate area under a curve.
- Apply to physics and other fields.
- Describe the relationship between derivatives and integrals (Fundamental Theorem of Calculus).
- Solve indefinite integrals.
Indefinite Integrals and Applications of Definite Integrals
- Use substitution to evaluate definite integrals.
- Use definite integrals to find the area between two curves.
- Use integral calculus to determine volumes, lengths of plane curves, and surface areas.
- Integrate to find work and fluid forces.
- Calculate moments and centers of mass using integration.
Transcendental Functions - Part 1
- Differentiate inverse functions.
- Differentiate logarithmic functions and exponential functions.
- Review Logarithmic Differentiation.
- Integrate logarithmic functions and exponential functions.
- Solve separable differential equations involving exponential change.
Transcendental Functions - Part 2
- Use L’Hopital’s rule to differentiate indeterminant rational functions.
- Differentiate inverse trigonometric functions and functions.
- Integrate inverse trigonometric functions.
- Solve exponential rates of growth problems.
Techniques of Integration - Part 1
- Evaluate integrals using integration by parts.
- Integrate trigonometric functions.
- Integrate using substitution with rational and trigonometric functions.
- Solve differential equations with Integration by parts in the solution, as well as first-order linear with constant coefficients.
Techniques of Integration - Part 2
- Use partial fractions to simplify integration of rational functions.
- Use integral tables to evaluate integrals.
- Estimate integrals with the Trapezoidal rule and Simpson’s rule.
- Solve improper integrals.
Calculus II Concept Review
- Apply the concepts presented in this course.
A prerequisite is required for this course. The purpose of a prerequisite is to ensure students have the knowledge and/or skills needed to be successful in the course. Students are required to provide proof of prerequisite during the enrollment/registration process. To meet to a course prerequisite requirement, a student must have successfully completed the prerequisite course at University of Phoenix, provide proof via transcript of completing a comparable course (at least 75% match) or higher level course with at least a grade of C at another institution or have a University of Phoenix approved Student Appeal on file with the University.
This course requires the prerequisite below. Click on the prerequisite course to review the course topics and objectives.
- MTH/280 – Calculus I OR
- equivalent or higher college mathematics course
During the checkout process you will be prompted to provide proof of the requirement(s). If you completed the prerequisite at another institution be prepared to upload an official/unofficial transcript. If you have questions about meeting the prerequisite requirements for this course please contact an enrollment representative at 888-484-1815.
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Transferability of credit is at the discretion of the receiving institution. It is the student’s responsibility to confirm whether or not credits earned at University of Phoenix will be accepted by another institution of the student’s choice.