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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
- Why integrating sin^2(wt) gives the half-period? - Physics Forums
Do you know what the integral of \sin^2x is? If you don't, use the cosine double angle formula \cos 2x = \cos^2x - \sin^2x and the Pythagorean identity \sin^2x + \cos^2x = 1 to express \sin^2x in terms of \cos 2x
- Integral of differential cross section over solid angle
The discussion revolves around finding the integral of the differential cross section, σ, starting from the expression for dσ dΩ = r²sin²θ and integrating over the solid angle Ω The context is within the subject area of physics, specifically dealing with integrals in the context of scattering theory Exploratory, Mathematical reasoning, Assumption checking Participants discuss the
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