Draw diagonal arrows from term n in column 1 to term n+1 in column two with alternating signs starting with +.Integrate f(x) repeatedly until you have the same number of terms as in the first column. ![]() Find the volume of the solid obtained by rotating R about the y-axis. 2) (b) (1.5 points) The region R is bound above by y x cos(x) and bound below by y: x sin(x) for x between 7 and 7. Integrate f(x) repeatedly until you have the same number of terms as in the first column. (2.5 points) Use the tabular method for repeated integration by parts to respond to the following prompts: (a) (1 point) Evaluate re 2003 + x) e2x dx.Differentiate p(x) repeatedly until you obtain 0, and list the results in the first column.Integrals of the form where p(x) is a polynomial can sometimes be evaluated using a method called Tabular Integration.Since the new integral is harder than the original, we made the wrong choice.Look at what happens when we make different choices for u and dv in example 1. If the new integral is harder that the original, you made the wrong choice.The acronym LIATE may help you remember the order.Logarithmic, Inverse Trig, Algebraic, Trig, Exponential.When the integrand is a product of two functions from different categories in the following list, you should make u the function whose category occurs earlier in the list. There is a useful strategy that may help when choosing u and dv.In general, there are no hard and fast rules for doing this it is mainly a matter of experience that comes from lots of practice. The first step in integration by parts is to choose u and dv to obtain a new integral that is easier to evaluate than the original.The first thing we will do is to choose one function for u and the other function will be dv. The two functions in the original problem we are integrating are u and dv.This is the way we will look at these problems.Now lets make some substitutions to make this easier to apply. ![]()
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