GATE 2025 MA – Question 34

Numerical Analysis · Numerical Differentiation and Integration · 1 mark · Numerical answer

Quadrature ∫₋₁¹f(x)dx=αf(−1)+βf(1)+γf′(−1)+δf′(1) is exact through degree three. Find 9(α²+β²+γ²+δ²) (integer).

Show answer and explanation

Correct answer: 20 to 20

Explanation

Exactness for 1,x,x²,x³ gives α+β=2; −α+β+γ+δ=0; α+β−2γ+2δ=2/3; −α+β+3γ+3δ=0. Solving gives α=β=1,γ=1/3,δ=−1/3. Required sum = 9(2+2/9)=**20**.

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