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.



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