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 transcript:

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 of f and is denoted by and where

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

III. Integral Formulas Indefinite Integral

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

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.

Ex.- Solve Proc:

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

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.

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?