Integrals
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Integrals PowerPoint PPT Presentation


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Integrals. Areas. What is an integral?. An integral is the generalized summation of a function between two boundaries definitely or indefinitely. In Physics, often the area under the curve is known as the integral In math, integral can find the summation of the curve.

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Integrals

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Integrals

Integrals

Areas


What is an integral

What is an integral?

  • An integral is the generalized summation of a function between two boundaries definitely or indefinitely.

  • In Physics, often the area under the curve is known as the integral

  • In math, integral can find the summation of the curve


Bruce s law for integral

Bruce’s Law for Integral

  • Do exactly the opposite of what you do to find a derivative…I mean it.

  • Example: take f(x) = axn

    To find the intregal of f(x):

    ∫f(x) = axn+1 + c

    n+1

    The “c” is any constant, it’s always there if it’s an indefinite (no boundaries) integral


Bruce s law for integral1

Bruce’s Law for Integral

  • Do exactly the opposite of what you do to find a derivative…I mean it.

  • Example: take f(x) = axn

    To find the intregal of f(x):

    ∫f(x) = axn+1 + c

    n+1

    The “c” is any constant, it’s always there if it’s an indefinite (no boundaries) integral


Cases

Cases

  • Fundamental Theorem of Calculus

  • Basically, given a function, to find the value between two boundary. Take the integral of the function and subtract the value of the two boundaries.

  • Ex: ∫ab f(x) = F(b) – F(a)


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