What is the Integral of 2^ (x)? - Physics Forums
Dec 5, 2003 · The integral of 2^x with respect to x is (1/ln (2)) * 2^x + C, where C is the constant of integration. This result is derived using the property that the derivative of a^x is ln (a) * a^x, allowing …
How to do integral for Cos(x^2)dx? - Physics Forums
Oct 22, 2006 · The integral of cos (x²) from 0 to infinity is equal to the integral of sin (x²) over the same limits, both yielding the result of (1/2)√ (π/2). This conclusion is derived using complex analysis and …
What is the Integral of -e^ (-x)? - Physics Forums
Sep 21, 2004 · Hi guys, I am looking in my calculus book, and it tells me in the example problem that the Integral of e^(-x)dx = -e^(-x) I don't see how u get this answer. I know the integral of e^x = e^x but …
Solving Integrals for e^-ax^2: (i), (ii) & (iii) - Physics Forums
Nov 9, 2006 · The discussion focuses on solving integrals of the form \ (\int_ {0}^ {\infty} e^ {-ax^2} x^n dx\) for \ (n = 2, 3, 4\) using differentiation and integration by parts. The integral \ (\int_ {0}^ {\infty} e^ …
Integral of 1 / (x^2 + 2) dx - 2) dx ? • Physics Forums
Sep 30, 2021 · The integral of the function ∫ 1 x 2 + 2 d x is evaluated using trigonometric substitution. The correct approach involves recognizing that this integral can be transformed into a standard form …
How do you integrate (r^2-x^2)^ (1/2) with a constant r?
Jun 18, 2004 · The integration of (r^2 - x^2)^ (1/2) with a constant r can be effectively solved using trigonometric substitution. Specifically, substituting x with r * sin (u) or r * cos (u) simplifies the …
Understanding the integral of 1/ (1+x^2) • Physics Forums
Aug 15, 2011 · The integral of 1/ (1+x²) is definitively arctan (x) + C, where C is the constant of integration. Substitution using x = tan (Θ) transforms the integral into a more manageable form, …
Integrating (x^2-1)^n: How to Get to the Answer? - Physics Forums
Aug 20, 2009 · The integral of the expression \ ( (-1)^n (2n)!/ (2^ {2n} (n!)^2) \int_ {-1}^ {1} (x^2-1)^n dx\) simplifies to \ (\frac {2} {2n+1}\) through a series of transformations and substitutions. The discussion …
What is the relationship between the integral and the area of half a ...
Jun 13, 2012 · Since you are integrating with respect to y, r^2 - x^2 = t^2 is a constant. So the integral becomes, \int_ {-t}^ {t} \sqrt {t^2-y^2}dy Now, the function you are integrating can be taken as, X = …
Why is integral of 1/z over unit circle not zero? - Physics Forums
Feb 23, 2012 · The integral of 1/z over the unit circle is equal to 2πi, contrary to the intuitive expectation that it should cancel out due to symmetry. This discrepancy arises because integration over a closed …