3-point Gaussian integration formula is given by:
$\int_{-1}^{1} f(x) d x \approx \sum_{j=1}^{3} A_{j} f\left(x_{j}\right)$ with $x_{1}=0, x_{2}=-x_{3}=-\sqrt{\frac{3}{5}} ; A_{1}=\frac{8}{9}, A_{2}=A_{3}=\frac{5}{9}$
This formula exactly integrates
(A) $f(x)=5-x^{7}$
(B) $f(x)=2+3 x+6 x^{4}$
(C) $f(x)=13+6 x^{3}+x^{6}$
(D) $f(x)=e^{-x^{2}}$
3-point Gaussian integration formula is given by:
$\int_{-1}^{1} f(x) d x \approx \sum_{j=1}^{3} A_{j} f\left(x_{j}\right)$ with $x_{1}=0, x_{2}=-x_{3}=-\sqrt{\frac{3}{5}} ; A_{1}=\frac{8}{9}, A_{2}=A_{3}=\frac{5}{9}$
This formula exactly integrates
(A) $f(x)=5-x^{7}$
(B) $f(x)=2+3 x+6 x^{4}$
(C) $f(x)=13+6 x^{3}+x^{6}$
(D) $f(x)=e^{-x^{2}}$