# Don't know how to start the problem

Gold Member
The question is : Determine the degree of precision of the formula for $$\int_{-1}^{1} f(x)dx$$~$$\frac{4}{3}f(-0.5)-\frac{2}{3}f(0)+\frac{4}{3}f(0.5)$$.
My guess is that I must answer like "the degree of precision is that this formula is exact for polynomials of grade $$\leqslant$$ 2", for example.
My attempt are just thoughts... Can't start. Watching the coefficients in the right side of the "approximation", it is similar to the Simpson's rule.

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Dick
Homework Helper
It is exact for degree of polynomial<=2. To check this put f(x)=ax^2+bx+c. I'll give you a hint. It's also exact for cubics. Can you show this the same way? Is it exact for quartics?

Gold Member
Thank you! Before reading your message I tried a quadratic one and it worked, then a cubic one but didn't worked (now I found my calculus error!) and then I gave up because I had the sentiment I wasn't proving anything. I didn't had the idea to put the f(x) as a general form like $$a_0x^3+a_1x^2+a_2x+a_3$$. Now it worked till cubic ones, so the degree of precision of the formula is 3.