Skip to content
Part BCSIR NET June 2024convolution-kernel-means-laplace

Convolution kernel means laplace

Let u be the solution of the Volterra integral equation ∫0\int_{0}ᵗ [½ +sin⁡(t−τ)]u(τ)dτ=sin⁡t+ \sin(t - \tau)] u(\tau) d\tau = \sin t. Then the value of u(1) is

  1. A.0✓ Correct
  2. B.1
  3. C.2
  4. D.2e⁻1^{1}

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests standard counterexample.

See pricing

50 are analysed free — try those first.

The trap it tests

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

Drill statements like this

Related counterexample: Every integral equation of the second kind has a unique solution

More on this topic

The chapter behind this: Integral equations: Fredholm vs Volterra — free to read

From Linear Integral Equations › Fredholm and Volterra equations

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

ShareWhatsAppTelegram