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- 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
- 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
- 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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