GATE 2020 ME (ME2) – Question 45

Engineering Mathematics · Numerical Methods: Algebraic equations, integration by trapezoidal and Simpson rules, ODE methods · 2 marks · Numerical answer

For $\int_0^{\pi/2}(8+4\cos x)\,dx$, find absolute percentage error of a trapezoidal-rule evaluation using only endpoints, to one decimal.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 5.1 to 5.5

Explanation

Exact integral is4π+4=16.56637. The endpoints are12 and8, so trapezoidal result is(π/2)(12+8)/2=5π=15.70796. Percentage error is100|5π−(4π+4)|/(4π+4)=**5.2%**. Divide by the exact value.