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

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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.