Can poles on the contour still be used with the residue theorem? Hi, I am trying to prove that I have the correct value of an integral of the form ${\int }_{0}^{2\pi }f(\mathrm{cos}\theta ,\mathrm{sin}\theta )d\theta$ I want to use the residue theorem, but I have one problem: all the literature I can find says that for contour integrals of this form, you can only use the residue theorem when the poles don't lie on the contour, and my poles are at z=0 and z
Electric Field Produced by a Finite Charged Wire - Physics Forums Homework Help Overview The problem involves calculating the electric field produced by a finite charged wire with a linear charge density at a specific point above its midpoint The context is rooted in electrostatics and requires the application of integral calculus to derive the electric field expression in terms of given parameters Discussion Character Exploratory, Mathematical reasoning
Why integrating sin^2(wt) gives the half-period? - Physics Forums In an exercise with included solution I can't understand how integrating sin^2(ωt) gives T(period) 2 \\intsin^2(ωt)dt = Period 2 I posted the whole problem below, because I had more doubts, but understood them typing up the problem I appreciate any help [SIZE="2"]YOU CAN
Understanding Integration of 1 (x^2 + a^2) and the Role of the Tan . . . There is a suggestion to evaluate the indefinite integral ∫ (1 (1+x²))dx as a starting point for understanding the integration of 1 (x² + a²) Participants discuss using the substitution x = tan (y) to compute the integral, indicating that this method is effective for transforming the integral into a more manageable form
What is the Integral of 2^ (x)? - Physics Forums The integral of 2^x with respect to x is (1 ln (2)) * 2^x + C, where C is the constant of integration This result is derived using the property that the derivative of a^x is ln (a) * a^x, allowing for the straightforward application of integration techniques By substituting 2^x with e^ (x * ln (2)), the integration process simplifies