The definite integral _1^3 1/xdx is evaluated using Trapezoidal rule with a step size of 1. The correct answer is __________ - General NAT PYQs Based Test - 27 : Numerical Methods (Integral Equations) | ExamTest.live

mediumNATPYQs Based Test - 27 : Numerical Methods (Integral Equations)General

1 mark

The definite integral 1 \int 3 \frac{1}{x} d x is evaluated using Trapezoidal rule with a step size of 1. The correct answer is __________

Correct Answer

1.16-1.17

Solution & Step-by-step Explanation

Concept: By trapezoidal rule, ** x_{0} \int x_{n} f (x) d x = \frac{h}{2} [(y_{0} + y_{n}) + 2 (y_{1} + y_{2} + \dots)] \dots (1) Calculation: Given:** h = 1 & y = \frac{1}{x} Table for calculating y₀, y₁, y₂, y₃ ......yₙ x 123 y = 1/x 1 \frac{1}{2} = 0.5 \frac{1}{3} = 0.3333 Designation y₀ y₁ y₂ Using equation (1), \Rightarrow 1 \int 3 \frac{1}{x} d x = \frac{1}{2} [(1 + \frac{1}{3}) + 2 (0.5)] = 1.167

x	1	2	3
y = 1/x	1	$\frac{1}{2} = 0.5$	$\frac{1}{3} = 0.3333$
Designation	y₀	y₁	y₂

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The definite integral 1 \int 3 \frac{1}{x} d x is evaluated using Trapezoidal rule with a step size of 1. The correct answer is __________