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Approximating Definite Integrals - Integration Techniques
In this section we have spent quite a bit of time on computing the values of integrals. Though, not all integrals can be calculated. A perfect instance is the subsequent definite integral.
Here we now need to talk a little bit about estimating values of definite integrals. We will seem at three different methods, even though one should already be well- known to you from your Calculus I days. We will build up all three methods for estimating
∫ba f (x) dx
by thinking of the integral like an area problem and by using known shapes to calculate the area within the curve. Let us get first develop the methods and then we will try to calculate the integral illustrated above.
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Dot Product- Vector The other topic for discussion is that of the dot product. Let us jump right into the definition of dot product. There is given that the two vectors a
Left-handed limit We say provided we can make f(x) as close to L as we desire for all x sufficiently close to a and x Note that the change in notation is extremely m
Ahmad borrowed $450000.00 at 3% compounded semi-annually for ten years to buy an apartment. Equal payments are made at the end of every six months. a) Determine the size of the se
Given f (x) = - x 2 + 6 x -11 determine each of the following. (a) f ( 2) (b) f ( -10) (c) f (t ) Solution (a) f ( 2) = - ( 2) 2 + 6(2) -11 = -3 (
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Some important issue of graph Before moving on to the next example, there are some important things to note. Firstly, in almost all problems a graph is pretty much needed.
Discontinuous Integrand- Integration Techniques Here now we need to look at the second type of improper integrals that we will be looking at in this section. These are integr
Parametric Equations and Curves Till to this point we have looked almost completely at functions in the form y = f (x) or x = h (y) and approximately all of the formulas that w
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