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Azienda News:
- 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 closed-form solutions of Equation looks like a lot of work And even WolframAlpha returns a tremendous
- 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 element in polar coordinates There are attempts to clarify why certain terms, such as 2π, do not
- Find Volume of Solid: Integral Rotation | y=1+sec x y=3
The discussion focuses on finding the volume of the solid formed by rotating the region bounded by the curves y=1+sec (x) and y=3 around the line y=1 The critical points of intersection are identified at x=-π 3 and x=π 3, which define the limits of integration The participants emphasize the need for clarity in the problem statement regarding the bounded region, as the curve y=3 intersects infinitely The solution involves using the disk or washer method for volume calculation
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