Question

Using Trapezoidal rule, calculate \int_{0}^{1}\frac{dx}{1+x^2} by dividing the interval ]1,0[ in 5 equal subintervals. Hence evaluate π.

13 Mar 2024
Answer :
Word Count : 408

To approximate the integral \(\int_{0}^{1} \frac{dx}{1+x^2}\) using the Trapezoidal rule with 5 equal subintervals, follow these steps:

1. **Divide the interval \([0, 1]\) into 5 equal subintervals**:
   The interval \([0, 1]\) is divided into 5 equal parts, so the width \(h\) of each subinterval is:
   \[
   h = \frac{1 - 0}{5} = 0.2
   \]

2. **Determine the \(x\) values**:
   The \(x\) values at the boundaries of the subintervals are:
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