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6.1 Indefinite Integrals and Slope Fields. I. The Indefinite Integral Let f be a derivative. The set of all antiderivatives of f is the indefinite integral.

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Presentation on theme: "6.1 Indefinite Integrals and Slope Fields. I. The Indefinite Integral Let f be a derivative. The set of all antiderivatives of f is the indefinite integral."— Presentation transcript:

1 6.1 Indefinite Integrals and Slope Fields

2 I. The Indefinite Integral Let f be a derivative. The set of all antiderivatives of f is the indefinite integral of f and is denoted by and where

3 II. The Indefinite Integral Continued Is one indefinite integral of f, namely the one whose value at a equals 0.

4 III. Integral Formulas Indefinite Integral

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9 IV. Properties of Indefinite Integrals 1.) Constant Multiple Rule- 2.) Sum/Difference Rule-

10 V. Solving Initial Value Problems Def.- Differential Equation – Any equation containing a derivative. To solve a differential equation means to find a function meeting all conditions.

11 Ex.- Solve Proc:

12 If given the initial condition (0, 2), then…

13 VI. Applications SPSE $1,000 is invested in an account that pays 6% yearly interest compounded continuously. How much money will be in the account after 25years? First, y(t) = money in the account at time t and y(0) = $1,000.

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15 A helicopter pilot drops a package 200 ft. above ground when the helicopter is rising at a speed of 20 ft./sec. How long does it take the package to hit the ground and what is its speed on impact?

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