in trpezoidal rule for numerical integration how you can find error
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.
2 ?
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.
simpson method
explain how to find the rule in a numerical pattern
Yes.
Integration by parts is the integration of the product rule of differentiation. Used to transform a non-simple derivative integral into a simple antiderivative integral.
False
False
Write them in order, then 1.3499 is labelled 0, 1,88221 is 1, 2.4596 is 2. etc . It's just the convention for labelling successive ordinates.
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.
Simpson's Rule is a good simple one that usually works well.
The zero error depends on the user, and the wear on the metre rule. Given that smaller rulers have about 2mm of material before the zero mark, wear is unlikely to exceed that without being noticed. The reading error is +/- 1 mm.