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- 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
- 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
- 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
- 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
- Integrating the Complex Expression: 1 (√(1-x²) · arcsin(x))
The discussion revolves around the integration of the complex expression \ (\int \frac {1} {\sqrt {1-x^2} \cdot \arcsin (x)} \, dx\) Participants explore various methods for solving the integral, including integration by parts and substitution techniques, while addressing misunderstandings and corrections related to the approach One participant suggests that the integral resembles the form
- 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
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