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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 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
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 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 • 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)
