Editing 2117: Differentiation and Integration
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'''{{w|Riemann integral|Riemann Integration}}''' | '''{{w|Riemann integral|Riemann Integration}}''' | ||
β | The Riemann integral is a definition of definite integration. <math>\sum_{i=0}^{n-1} f(t_i) \left(x_{i+1}-x_i\right).</math> Elementary textbooks on calculus sometimes present finding a definite integral as a process of approximating an area by strips of equal width and then taking the limit as the strips become narrower. Riemann integration removes the requirement that the strips have equal width, and so is a more flexible definition. However there are still many functions for which the Riemann integral doesn't converge, and consideration of these functions leads to the {{w|Lebesgue | + | The Riemann integral is a definition of definite integration. <math>\sum_{i=0}^{n-1} f(t_i) \left(x_{i+1}-x_i\right).</math> Elementary textbooks on calculus sometimes present finding a definite integral as a process of approximating an area by strips of equal width and then taking the limit as the strips become narrower. Riemann integration removes the requirement that the strips have equal width, and so is a more flexible definition. However there are still many functions for which the Riemann integral doesn't converge, and consideration of these functions leads to the {{w|Lebesgue Integral}}. Riemann integration is not a method of calculus appropriate for finding the anti-derivative of an elementary function. |
'''{{w|Stokes' Theorem}}''' | '''{{w|Stokes' Theorem}}''' |