GATE 2021 MA – Question 63

Numerical Analysis · Numerical Differentiation and Integration · 2 marks · Numerical answer

The quadrature ∫₀²x f(x)dx≈αf(0)+βf(1)+γf(2) is exact for every polynomial f of degree at most 2. Find 2β−γ.

Show answer and explanation

Correct answer: 2 to 2

Explanation

For f=1,x,x², exactness gives α+β+γ=2,β+2γ=8/3,β+4γ=4. Subtraction gives γ=2/3, then β=4/3 and α=0. Hence 2β−γ=8/3−2/3=**2**.

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