Integration of x^2 (xsinx+cosx)^2 - Physics Forums Hi everyone, First of all, this isn't really a "homework", I've completed my calculus course and I'm just curious about this problem Homework Statement \\int\\frac{x^{2}}{(xsinx+cosx)^{2}} dx Homework Equations Trigonometric substitutions, integration by parts maybe? The
What is the Integral of -e^ (-x)? - Physics Forums A later reply discusses the integral of 2x e^ (x^2) and questions whether the integral of f' (x)e^f (x) is always e^f (x), regardless of the nature of f' (x) Participants express that one cannot derive integrals without prior knowledge of their results, highlighting the challenge of integration
Prove that the integral is equal to ##\pi^2 8## • Physics Forums Prove ∫ 0 2 4 1 x x 2 arcsin (x 1) (x 1 + x 9 16 x) 1 2 x d x = π 2 8 Let The representation integral of is Plugging identity above into with , we obtain Since the integrand is non-negative and continuous over the rectangular domain ( is the root of the numerator), Fubini's Theorem allows us to interchange the order: where and are the closed solutions of the equation Now, computing the closed-form solutions of Equation looks like a lot of work And even WolframAlpha returns a tremendous
Why the Chern numbers (integral of Chern class) are integers? One participant provides an example involving the tangent bundle of the 2-sphere to illustrate how the integral of the curvature form relates to the first Chern class and the Euler characteristic
How Do You Integrate (dx dt) dx in Physics Problems? Participants explore different approaches to rewriting the integral and the implications of variable dependencies One participant asks how to integrate ∫ b (dx dt) ⋅ dx, mentioning difficulty in substituting dx with v dt
Integral Over all Space for Charge Density - Exponential Fun The problem involves finding the charge density from a given electric field described by E = C e^ {-br} r^2 and integrating it over all space to demonstrate that the result is zero The context is rooted in electromagnetism, specifically in the application of Gauss's law and charge density calculations Exploratory, Assumption checking, Mathematical reasoning The original poster attempts to derive the charge density using the divergence of the electric field and integrating over all space