GATE 2023 MA – Question 29

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

For fixed real c, the trapezoidal-rule value of ∫₀²(9x²−5cx⁴)dx equals the exact integral. Find c to two decimals.

Show answer and explanation

Correct answer: 0.24 to 0.26

Explanation

Exact integral=24−32c. One-panel trapezoidal value=(2/2)[f(0)+f(2)]=36−80c. Equating gives 48c=12, hence **0.25**.

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