Integration is a mathematical concept that involves finding the area under a curve by using a definite integral. Riemann sums, on the other hand, are a method of approximating the area under a curve by dividing it into smaller rectangles and adding up their areas.
Integration is generally considered more accurate because it takes into account the entire curve, while Riemann sums only approximate the area using smaller rectangles. However, with a large enough number of rectangles, Riemann sums can also provide accurate results.
Riemann sums are useful for approximating the area under a curve when the function cannot be easily integrated, or when the integral cannot be solved analytically. They are also relatively easy to understand and implement.
Integration should be used when an exact solution is needed, or when the function can be easily integrated. It is also more efficient for calculating the area under a curve compared to Riemann sums, which require a large number of rectangles for accurate results.
No, Riemann sums can only be used for continuous functions. This is because the method relies on dividing the area into smaller rectangles and adding their areas, which is not possible for functions with discontinuities.