in trpezoidal rule for numerical integration how you can find error
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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.
Yes.
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.
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.
The numerical value is the same as the quotient of the two positive equivalents but the sign is always negative.