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Why is Trapezoidal rule better than Riemann left right rule?
It's because the diagonal line on each trapezoid cuts down on the error of your area estimation. It is the average of the left and right rules.
Use Trapezoidal rule to evaluate the approximate values of definite integrals?
Yes.
How is integration through substitution related to the Chain Rule?
i love wikipedia!According to wiki: In calculus, integration by substitution is a method for finding antiderivatives and integrals. Using the fundamental theorem of calculus often requires finding an antiderivative. For this and other reasons, integration by substitution is an important tool for mathematicians. It is the counterpart to the chain rule of differentiation.
What is the Definition or formula of Theta method?
theta method is a numerical method for solving ODE ( y'(t) = f(t, y(t)) ) given by (y_{n+1} - y_{n})/ h = \Theta * f (t_{n+1}, y_{n+1}) + (1 - \Theta) * f (t_{n}, y_{n}). In particular, for \Theta = 0 it is the explicit Euler method (i.e. the forward Euler method), \Theta = 1/2 is the trapezoidal rule.
What is the rule for dividing rational numbers with different signs?
The numerical value is the same as the quotient of the two positive equivalents but the sign is always negative.
