http://www.bing.com:80/search?q=Athapoo+FlowerSearch resultshttp://www.bing.com:80/s/a/rsslogo.gifhttp://www.bing.com:80/search?q=Athapoo+FlowerCopyright © 2026 Microsoft. All rights reserved. These XML results may not be used, reproduced or transmitted in any manner or for any purpose other than rendering Bing results within an RSS aggregator for your personal, non-commercial use. Any other use of these results requires express written permission from Microsoft Corporation. By accessing this web page or using these results in any manner whatsoever, you agree to be bound by the foregoing restrictions.https://www.physicsforums.com/threads/integration-of-x-2-xsinx-cosx-2.745830/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...Sun, 05 Apr 2026 04:16:00 GMThttps://www.physicsforums.com/threads/what-is-the-integral-of-e-x.43963/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.Mon, 06 Apr 2026 06:52:00 GMThttps://www.physicsforums.com/threads/prove-that-the-integral-is-equal-to-pi-2-8.1080977/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 ...Tue, 07 Apr 2026 17:14:00 GMThttps://www.physicsforums.com/threads/why-integrating-sin-2-wt-gives-the-half-period.618662/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.Sun, 05 Apr 2026 04:59:00 GMThttps://www.physicsforums.com/threads/how-to-integrate-1-x-2-1-dx.329317/The discussion revolves around the integration of the function \ (\int\frac {1} {x^2 + 1} \ dx\), which falls under the subject area of calculus, specifically focusing on integration techniques. Exploratory, Mathematical reasoning, Problem interpretation Participants discuss various methods for integration, including substitution and trigonometric substitution. Some express difficulty in eliminating the variable \ (x\) from the integral. Questions arise about the effectiveness of these ...Sat, 04 Apr 2026 17:18:00 GMThttps://www.physicsforums.com/threads/why-is-integral-of-1-z-over-unit-circle-not-zero.580753/The discussion revolves around the integral of the function 1/z over the unit circle, questioning why it does not equal zero despite intuitive reasoning that suggests cancellation of contributions from points on opposite sides of the circle. Participants explore concepts related to integration, odd functions, and the implications of singularities in the context of complex analysis. Some participants assert that the integral of 1/z over the unit circle equals 2∏i, while others feel that ...Sun, 05 Apr 2026 16:05:00 GMThttps://www.physicsforums.com/threads/integral-of-trig-functions-over-a-period.836332/The discussion revolves around the integral of trigonometric functions, specifically the product of cosines with different arguments, over a specified interval. Participants explore the conditions under which these integrals vanish, the implications of integrating over a period, and the properties of periodic functions. One participant seeks an intuitive understanding of why the integral of cos ( (2*pi*x)/a)*cos ( (4*pi*x)/a) vanishes over the interval from 0 to a, questioning the meaning of ...Sat, 04 Apr 2026 15:02:00 GMThttps://www.physicsforums.com/threads/find-volume-of-solid-integral-rotation-y-1-sec-x-y-3.635152/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 ...Wed, 08 Apr 2026 04:56:00 GMThttps://www.physicsforums.com/threads/circled-part-formula-in-double-integral-explaining-the-use-of-da-in-polar-form.878343/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 ...Wed, 08 Apr 2026 16:37:00 GMThttps://www.physicsforums.com/threads/how-do-you-integrate-dx-dt-dx-in-physics-problems.827868/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.Thu, 02 Apr 2026 16:16:00 GMT