math 260 lab 6 - MATH260Week 6 Lab Name Kong Lee...

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MATH260—Week 6 Lab Name: Kong Lee 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 b.) f(x) = 5x – 6
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?
4) What do the derivatives of the following antiderivatives have in common? – 11
Directions: Look at the examples, then find each of the integrals below. 3 x + 5 dx F(x) = 3 2 x 2 + 5 x + C 4 x 3 6 xdx F(x) = x 4 3 x 2 + C 3 x + 2 x 2 dx F(x) = 2 x 3 2 2 x + C 4 x 5 ¿ 3 dx ¿ ¿ F(x) = 4 x 5 ¿ 3 + C 1 12 ¿ Well because the c satisfy the whole answer of the equation which includes an family’s equation. 6) Find the integral for f ( x )= x x 2 + 7 x 1 . Show all work. + 4
Integration by Substitution If part of the function is a derivative of the other part of the function, then integration by substitution can be applied. If the form is true, the following method will apply. 1) Label part of the function u and then find du, the derivative of u.

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