According to the first part of the fundamental theorem of...

This preview shows page 1 - 3 out of 11 pages.

We have textbook solutions for you!
The document you are viewing contains questions related to this textbook.
Calculus of a Single Variable
The document you are viewing contains questions related to this textbook.
Chapter 5 / Exercise 54
Calculus of a Single Variable
Edwards/Larson
Expert Verified
MATH260—Week 6 Lab Name: Antiderivatives According to the first part of the fundamental theorem of calculus, the antiderivative reverses the derivative. If f(x) is a derivative, F(x) is the antiderivative. Directions: Look at the examples below and answer questions 1 and 2. Let f(x) be a derivative and F(x) be the anitderivative. a.) f(x) = 3x 2 F ( x )= 3 x 2 + 1 2 + 1 = x 3 b.) f(x) = 5x – 6 F ( x )= 5 x 1 + 1 1 + 1 6 x 0 + 1 1 = 5 2 x 2 6 x c.) f ( x )= 3 x 1 x 4 F ( x )= x 1 3 + 3 3 4 3 x 4 + 1 3 = 3 4 x 4 3 + 1 3 x 3
2) Find the antiderivative of f(x) = 3x 5 + x – 4. Show all work.
3) How is an antiderivative related to a derivative? How can that relationship help you to check your antiderivatives and integrals answers?
We have textbook solutions for you!
The document you are viewing contains questions related to this textbook.
Calculus of a Single Variable
The document you are viewing contains questions related to this textbook.
Chapter 5 / Exercise 54
Calculus of a Single Variable
Edwards/Larson
Expert Verified
4) What do the derivatives of the following antiderivatives have in common? F(x) = 3x 2 + 5 , G(x) = 3x 2 + 9 , H(x) = 3x 2 – 11
Indefinite Integrals: f ( x ) dx = F ( x )+ C Used for finding the general form of the antiderivative.
Directions: Look at the examples, then find each of the integrals below. C x

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture