The GATE Grind

GATE 2021 MN – Question 31

Engineering Mathematics · Numerical Methods · 1 mark · Numerical answer

Approximate $I=\int_0^4\sqrt{x}\,dx$ by Simpson’s 1/3 rule with two subintervals. Round to three decimals.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 5.000 to 5.200

Explanation

The step is h=(4−0)/2=2. Values at 0, 2, 4 are 0, √2, 2. Simpson’s rule gives $I\approx(2/3)(0+4\sqrt2+2)=5.1045695$, or 5.105. This is the requested two-subinterval approximation, not the exact integral 16/3.

More Numerical Methods questions

All Numerical Methods questions →