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

In the range: 1.16 - 1.17

Concept:

By trapezoidal rule,

**$\underset{x_0}{\overset{x_n}{\int }}f\left(x\right)dx=\frac{h}{2}\left[\left(y_0+y_n\right)+2\left(y_1+y_2+\dots \right)\right]\dots \left(1\right)$

Calculation:

Given:**

h = 1 & $y=\frac{1}{x}$

Table for calculating y₀, y₁, y₂, y₃ ......yₙUsing equation (1),

$\Rightarrow \underset{1}{\overset{3}{\int }}\frac{1}{x}dx=\frac{1}{2}\left[\left(1+\frac{1}{3}\right)+2\left(0.5\right)\right]=1.167$