MathProblemsBank

i.2.33 Integrals depending on a parameter

condition: Investigate at what values ​​\( p \) converges and at what values ​​the integral over the parameter diverges. \[ \int_{\pi / 4}^{+\infty} \frac{\cos (2 x) d x}{(4 x-\pi)^{2 p}\left(x^{2}+x\right)} \text {. } \]

Integrals depending on a parameter, often referred to as parameter-dependent integrals or definite integrals with parameters, involve the integration of a function where one or more parameters are present. These parameter-dependent integrals can lead to a variety of problems and challenges. Here you can find problems related to convergence and divergence, calculation, limits, parametric integration and differentiation of parameter-dependent integrals. Also, there are usage and properties of Euler, Frullani, Poisson, Laplace, and Dirichlet integrals.

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