GATE XE (Engineering Sciences) 2022 - Question 21

Section: Engineering Mathematics | Type: NAT | Marks: 2

If the quadrature rule න𝑓ሺ𝑥ሻ𝑑𝑥 ଵି ଵ ൎ𝑓ሺ𝛼ሻ൅ 𝛾 𝑓ሺ𝛽ሻ, where 𝛼, 𝛽 and 𝛾 are real constants, is exact for all polynomials of degree ൑3, then 𝛾൅3 ሺ𝛼ଶ൅ 𝛽ଶሻ൅ሺ𝛼ଷ൅𝛽ଷሻ is equal to _______.

Answer: 3