lecture2_1_13.pdf

lecture2_1_13.pdf - Outline Introduction Integral...

  • No School
  • AA 1
  • 6

This preview shows page 1 - 6 out of 6 pages.

Outline Introduction Integral Applications I Techniques Applications II Infinite series The Fundamental Calculus Theorem, Part 1 The Fundamental Calculus Theorem, Part 1 Theorem Assume that f ( x ) is continuous on [ a , b ] . If F ( x ) is an antiderivative of f ( x ) on [ a , b ] then b a f ( x ) dx = F ( b ) F ( a ) . Dr. Vasileios Maroulas Assistant Professor Department of Mathematics University of Tennessee [email protected] Calculus II-Math 142
Image of page 1

Subscribe to view the full document.

Outline Introduction Integral Applications I Techniques Applications II Infinite series The Fundamental Calculus Theorem, Part 2 Theorem Assume that f ( x ) is continuous on an open interval I and let a I. Then the area function A ( x ) = x a f ( t ) dt is an antiderivative of f ( x ) on I, i.e. A ( x ) = f ( x ) . Equivalently, d dx x a f ( t ) dt = f ( x ) . Furthermore, A ( x ) satisfies the initial condition A ( a ) = 0 . Dr. Vasileios Maroulas Assistant Professor Department of Mathematics University of Tennessee [email protected] Calculus II-Math 142
Image of page 2
Outline Introduction Integral Applications I Techniques Applications II Infinite series The Fundamental Calculus Theorem, Part 2 Dr. Vasileios Maroulas
Image of page 3

Subscribe to view the full document.

Image of page 4
Image of page 5

Subscribe to view the full document.

Image of page 6
  • Fall '19
  • Calculus, Indian mathematics, Express f, Dr. Vasileios Maroulas

{[ 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