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The expression is an illustration of definite integrals
The approximated value of the definite integral is 0.0059
<h3>How to evaluate the definite integral?</h3>The definite integral is given as:
For arctan(x), we have the following series equation:
Multiply both sides of the equation by x^3.
So, we have:
Apply the law of indices
Evaluate the product
Introduce the integral sign to the equation
Integrate the right hand side
Expand the equation by substituting 1/2 and 0 for x
Evaluate the power
The nth term of the series is then represented as:
Solve the series by setting n = 0, 1, 2, 3 ..........
..............
At n = 2, we can see that the value of the series has 4 zeros before the first non-zero digit
This means that we add the terms before n = 2
This means that the value of to 4 decimal points is
Evaluate the difference
Approximate to four decimal places
Hence, the approximated value of the definite integral is 0.0059
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