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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
  • 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 is the distance calculation multiplied by one half in this physics . . .
    The discussion revolves around the reasoning behind the factor of one half in the distance calculation for uniformly accelerated motion in physics Participants explore various mathematical and conceptual explanations related to this factor, including algebraic and calculus-based approaches Some participants explain that the factor of one half arises from considering the average velocity of
  • 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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