We derive an approximate solution for hypersingular integrals of the
first kind. Chebyshev polynomials of the second kind are used to
construct the interpolating polynomial. In turn, this polynomial
approximates the crack opening displacement function of the density
function. A collocation method is implemented, with the zeros of the
Chebyshev polynomial of the first kind as the collocation points. As a
result of these implementations, the whole integral equation is
approximated by a system of algebraic equations which is mathematically
tractable. The application and accuracy of the present method are
illustrated with some relevant examples.