What are the advantages of using numerical integration (Trapezium rule, Simpson's rule and so on) over direct integration?

Numerical methods are particularly useful to solve complex problems which are sometimes difficult or impossible to solve analytically. It is also a quicker way of solving the problem rather than using formulas. Moreover it gives a good approximation provided the area is divided into reasonable number of strips. The greater the number of strips the better the approximation is.

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Answered by Priyanka A. Maths tutor

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