Integrate product of heaviside function and function of x

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Discussion Overview

The discussion revolves around the integration of the product of the Heaviside function and a function of x, specifically focusing on both indefinite and definite integrals. Participants explore different scenarios and conditions under which the integration is performed.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant inquires about the integration of the product of a function f(x) and the Heaviside function H(x).
  • Another participant clarifies the distinction between definite and indefinite integrals, suggesting that for the indefinite integral, the result is 0 for x < 0 and the integral of f(x) for x > 0.
  • A participant presents a specific definite integral involving the Heaviside function and asks for further assistance.
  • Another participant notes that if a > 0, the integral's bounds are (π, 2π), while for a < 0, the bounds are (0, π), indicating that in both cases the integrand no longer includes the Heaviside function.

Areas of Agreement / Disagreement

Participants express differing views on the bounds of the definite integral based on the value of a, indicating that multiple competing views remain regarding the integration process.

Contextual Notes

The discussion does not resolve the implications of the Heaviside function in the context of the specific integral presented, and assumptions regarding the behavior of f(x) are not fully explored.

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How would you integrate product of heaviside function and function of x

i.e. int[f(x)H(x)dx]

Thanks
 
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Are you looking for definite integral or indefinite?

For indefinite, the integral=0 for x < 0 and = the integral of f(x) for x > 0.

For definite integral, integral of f(x) with lower bound ≥ 0.
 
Thanks

The integral is \int_{0}^{2\pi} a^2(sint)^3H(-asint)dt

Help !?
 
If a > 0, integral is (π,2π), while for a < 0, integral is (0,π). In both cases the integrand is now without H.
 

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