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
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
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
Circled Part Formula in Double Integral: Explaining the Use of dA in . . . The discussion revolves around the use of the differential area element dA in the context of double integrals, specifically in polar coordinates Participants are examining why dA can be expressed as r (dr) (dθ) and the implications of this transformation in relation to the area of a circle Participants are questioning the relationship between the area of a circle and the differential area