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Who invented Riemann sum?
Riemann did.
Is finding the Riemann Sum of a curve just finding the midpoint rectangular approximation?
It could be. In addition to a Midpoint Rectangular Riemann Sum there is also a Left Rectangular Riemann Sum, a Right Rectangular Riemann Sum, and a Trapezoidal Riemann Sum. When you are asked to compute a Riemann Sum, you must choose from the above list depending on the specific question, your teacher's preferences, and/or your own preferences.
What causes hypothesis to be rejected?
We have two types of hypothesis i.e., Null Hypothesis and Alternative Hypothesis. we take null hypothesis as the same statement given in the problem. Alternative hypothesis is the statement that is complementary to null hypothesis. When our calculated value is less than the tabulated value, we accept null hypothesis otherwise we reject null hypothesis.
What mathematicians helped to discover alternatives to euclidean geometry in the nineteenth century?
Nikolai Lobachevsky and Bernhard Riemann
If we reject the null hypothesis what can we conclude about the alpha risk?
If we reject the null hypothesis, we conclude that the alternative hypothesis which is the alpha risk is true. The null hypothesis is used in statistics.
