In the following an integral has been evaluated using Cauchy residue theorem which seems enough. Why is there a need to parametrise the contour to evaluate the same integral i.e. what is the point in this ?
2026-03-28 16:13:32.1774714412
Why is there a need to parametrize the contour when we can get the answer using cauchy residue theorem?
59 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in INTEGRATION
- How can I prove that $\int_0^{\frac{\pi}{2}}\frac{\ln(1+\cos(\alpha)\cos(x))}{\cos(x)}dx=\frac{1}{2}\left(\frac{\pi^2}{4}-\alpha^2\right)$?
- How to integrate $\int_{0}^{t}{\frac{\cos u}{\cosh^2 u}du}$?
- Show that $x\longmapsto \int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha }}dy$ is integrable.
- How to find the unit tangent vector of a curve in R^3
- multiplying the integrands in an inequality of integrals with same limits
- Closed form of integration
- Proving smoothness for a sequence of functions.
- Random variables in integrals, how to analyze?
- derive the expectation of exponential function $e^{-\left\Vert \mathbf{x} - V\mathbf{x}+\mathbf{a}\right\Vert^2}$ or its upper bound
- Which type of Riemann Sum is the most accurate?
Related Questions in CONTOUR-INTEGRATION
- contour integral involving the Gamma function
- Find contour integral around the circle $\oint\frac{2z-1}{z(z-1)}dz$
- prove that $\int_{-\infty}^{\infty} \frac{x^4}{1+x^8} dx= \frac{\pi}{\sqrt 2} \sin \frac{\pi}{8}$
- Intuition for $\int_Cz^ndz$ for $n=-1, n\neq -1$
- Complex integral involving Cauchy integral formula
- Contour integration with absolute value
- Contour Integration with $\sec{(\sqrt{1-x^2})}$
- Evaluating the integral $\int_0^{2\pi}e^{-\sqrt{a-b\cos t}}\mathrm dt$
- Integral of a Gaussian multiplied with a Confluent Hypergeometric Function?
- Can one solve $ \int_{0}^\infty\frac{\sin(xb)}{x^2+a^2}dx $ using contour integration?
Related Questions in PARAMETRIZATION
- How might I find, in parametric form, the solution to this (first order, quasilinear) PDE?
- parameterization of the graph $y=x^2$ from (-2,4) to (1,1)
- How can I prove that the restricted parametrization of a surface in $\mathbb{R}^{3}$ ia a diffeomorphism?
- Is it possible to construct the equation of a surface from its line element?
- Arc length of curve of intersection between cylinder and sphere
- Variational Autoencoder - Reparameterization of the normal sampling
- Sweet spots for cubic Bezier curve.
- Sketch the parametrised curve $C = \{(1-e^{-t},e^{-2t}):t\in [0,\infty]\}$
- Finding a parametrization of the curve of intersection between two surfaces
- Finding Parametric Equations for the right side of Hyperbola
Related Questions in CAUCHY-INTEGRAL-FORMULA
- Find contour integral around the circle $\oint\frac{2z-1}{z(z-1)}dz$
- Evaluating a complex contour integral
- Show $f(w)=\frac{1}{2\pi i}\int_{\partial \Omega} f(z)\frac{g'(z)}{g(z)-g(w)}\,dz$ for $w\in\Omega$
- on Complex Integration $\int_{\gamma}\frac{dz}{z^{2}-1}$
- Is $F$ continuous on the closed unit disk $D(0, 1)$?
- Solving recurrence relations using generating functions with complex analysis
- Cauchy integral formula for not necessarily star-shaped regions
- Show that, if $f(z)$ is a polynomial with $f(z)=\sum_{n=0}^{k} a_{n}z^{n} $ for some $k \in \mathbb{N}$ that...
- Cauchy's differentiation formula
- Application of Morera's theorem?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?