5_4 - Section 5.4 Indenite Integrals and the Net Change...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 5.4: Indefinite Integrals and the Net Change Theorem Instructor: Ms. Hoa Nguyen ([email protected]) Reminder about the Fundamental Theorem of Calculus 1. If g ( x ) = x a f ( t ) dt , then g ( x ) = d dx x a f ( t ) dt = f ( x ). 2. b a f ( x ) dx = F ( b ) - F ( a ) where F is any antiderivative of f , i.e., F = f or F = f ( x ) dx (indefinite integral). The difference between indefinite and definite integrals A definite integral b a f ( x ) dx is a number . An indefinite integral f ( x ) dx is a function (or family of functions). The second part of the Fundamental Theorem of Calculus shows the connection between these two integrals: b a f ( x ) dx = F ( b ) - F ( a ) = F ( x )] b a = f ( x ) dx ] b a Table of Indefinite Integrals (check the hand-out) Example 1 of Section 5.4 (textbook): Example 2 of Section 5.4 (textbook): Example 3 of Section 5.4 (textbook): Example 4 of Section 5.4 (textbook): Example 5 of Section 5.4 (textbook): Applications The Net Change Theorem The integral of a rate of change is the net change: b a F ( x ) dx = F ( b ) - F ( a ). Example : If V ( t ) is the volume of water in a reservoir at time t , its derivative V ( t ) is the rate at which water flows into the reservoir at time t . So t 2 t 1 V (
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern