# Solving an integral with four point Gauss-Chebyshev

I am struggling with this question as in our notes it shows how to solve Gauss-Chebyshev integrals of the form $$\int_{-1}^{1}\frac{f(x)}{\sqrt{1-x^2}}dx$$ , however this is different.

$$\text{Solve the following using four point Gauss-Chevyshev quadrature: }\int_{0}^{\pi} \frac{\sin y}{\sqrt{\pi(1-y)}}dy$$

So far I have worked out the four integration points using the formula $$x_k = \cos({\frac{2k+1}{4}}.\frac{\pi}{4})$$ and I also know that the weight for each point is $$w_k=\frac{\pi}{4}.$$ I also know that the final answer is roughly 1.48281.

Help or a guided solution would be appreciated.

Thanks