Here are the essential concepts you must grasp in order to answer the question correctly.
Properties of Integrals
The properties of integrals, particularly the linearity property, state that the integral of a constant multiplied by a function can be factored out. This means that β«a^b kΖ(π) dπ = kβ«a^b Ζ(π) dπ, where k is a constant. This property simplifies the evaluation of integrals by allowing constants to be taken outside the integral.
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Definite Integrals
Definite integrals represent the signed area under a curve between two limits. The notation β«a^b Ζ(π) dπ indicates the integral of the function Ζ(π) from the lower limit a to the upper limit b. The result of a definite integral is a number that quantifies this area, which can be positive, negative, or zero depending on the function's behavior over the interval.
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Definition of the Definite Integral
Additivity of Integrals
The additivity property of integrals states that the integral over an interval can be split into the sum of integrals over subintervals. Specifically, β«a^c Ζ(π) dπ = β«a^b Ζ(π) dπ + β«b^c Ζ(π) dπ for any point b between a and c. This property is useful for evaluating integrals over larger intervals by breaking them down into smaller, manageable parts.
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Additional Rules for Indefinite Integrals
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