Local Truncation error We have error formulas for Gaussian Quadrature and polynomial interpolation with 10 Gaussian points, use them to derive formulas for the local truncation error, where $$P = \frac{f^n(\xi)}{n!}\prod_{i=0}^{n}(t-t_i)$$ is the error for Polynomial interpolation, 
and error of Gaussian Quadrature: 
$$Q = \frac{(b-a)^{2n+1}(n!)^4}{(2n+1)![(2n)!]^3}$$
How can I derive the formula for local error truncation using error formula above?
Are you in Math 128B with Professor Strain? 

If I'm not mistaken, I think this is the problem he's trying to solve:
https://math.berkeley.edu/~strain/128b.S15/p10.pdf

Here are some notes on the spectral integration method that must be used:
https://math.berkeley.edu/~strain/128b.S15/bvp.pdf

Some thoughts in the right direction: You're integrating over $[a, a + Ih]$ and $[a + (I+1)h, b]$ using Gaussian Quadrature, so you know the error for that exactly. How do you find the error of the spectral integration method that works over $[a + Ih, s_{Im + i}]$?
Are you in Math 128B with Professor Strain? 

If I'm not mistaken, I think this is the problem he's trying to solve:
https://math.berkeley.edu/~strain/128b.S15/p10.pdf

Here are some notes on the spectral integration method that must be used:
https://math.berkeley.edu/~strain/128b.S15/bvp.pdf

Some thoughts in the right direction: You're integrating over $[a, a + Ih]$ and $[a + (I+1)h, b]$ using Gaussian Quadrature, so you know the error for that exactly. How do you find the error of the spectral integration method that works over $[a + Ih, s_{Im + i}]$?