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Let u be the solution of the Volterra integral equation \(\rm \int_0^t\left[\frac{1}{2}+\sin (t-\tau)\right]u(\tau)d\tau=\sin t\)

Then the value of u(1) is

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Option 1 : 0
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The Correct answer is (1).

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More Fredholm and Volterra Integral Equation Questions

Q1.Let u be the solution of the Volterra integral equation \(\rm \int_0^t\left[\frac{1}{2}+\sin (t-\tau)\right]u(\tau)d\tau=\sin t\) Then the value of u(1) is

More Linear Integral Equations Questions

Q1.Let u be the solution of the Volterra integral equation \(\rm \int_0^t\left[\frac{1}{2}+\sin (t-\tau)\right]u(\tau)d\tau=\sin t\) Then the value of u(1) is
Q2.For the unknown y : [0, 1] → ℝ, consider the following two-point boundary value problem: \(\rm \left\{\begin{aligned}\rm y^{\prime \prime}(x)+2 y(x) & =0 \quad \text { for } \rm x ∈(0,1), \\ \rm y(0) & =\rm y(1)=0 .\end{aligned}\right.\). It is given that the above boundary value problem corresponds to the following integral equation: y(x) = 2\(\displaystyle\int_0^1\) K(x, t) y(t) dt for x ∈ [0, 1]. Which of the following is the kernel K(x, t)?

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