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Understanding Indefinite Integrals: Formulas, Properties & Applications

Explore indefinite integrals, antiderivatives of derivatives, integral formulas, solving initial value problems, and real-life applications such as compound interest and falling objects. Enhance your understanding of integral calculus concepts.

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Understanding Indefinite Integrals: Formulas, Properties & Applications

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  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

  5. Indefinite Integral

  6. Indefinite Integral

  7. Indefinite Integral

  8. Indefinite Integral

  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.

  14. 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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