Solved: The Two-Point Gaussian Quadrature Approximation for is (a) Use this formula to
Chapter 0, Problem 6(choose chapter or problem)
The Two-Point Gaussian Quadrature Approximation for f is
\(\int_{-1}^{1} f(x) d x \approx f\left(-\frac{1}{\sqrt{3}}\right)+f\left(\frac{1}{\sqrt{3}}\right)\)
(a) Use this formula to approximate \(\int_{-1}^{1} \cos x d x\). Find the error of the approximation.
(b) Use this formula to approximate \(\int_{-1}^{1} \frac{1}{1+x^{2}} d x\).
(c) Prove that the Two-Point Gaussian Quadrature Approximation is exact for all polynomials of degree 3 or less.
Text Transcription:
int_-1^1 f(x) dx approx f(-1/sqrt 3)+f(1/sqrt 3)
int_-1^1 cos x dx
int_-1^1 1/1+x^2 dx
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer