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

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Chapter 4 / Exercise 26
Calculus
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MATH260—Week 6 Lab Name: Samuel Swapp 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 antiderivative. 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.
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Chapter 4 / Exercise 26
Calculus
Stewart 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
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