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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.
Tangents with Parametric Equations In this part we want to find out the tangent lines to the parametric equations given by X= f (t) Y = g (t) To do this let's first r
Combined Mean And Standard Deviation Occasionally we may need to combine 2 or more samples say A and B. Therefore it is essential to identify the new mean and the new standard
Determine a particular solution for the subsequent differential equation. y′′ - 4 y′ -12 y = 3e5t + sin(2t) + te4t Solution This example is the purpose that we've been u
from 0->1: Int sqrt(1-x^2) Solution) I=∫sqrt(1-x 2 )dx = sqrt(1-x 2 )∫dx - ∫{(-2x)/2sqrt(1-x 2 )}∫dx ---->(INTEGRATION BY PARTS) = x√(1-x 2 ) - ∫-x 2 /√(1-x 2 ) Let
Determination of the Regression Equation The determination of the regression equation such given above is generally done by using a technique termed as "the method of least sq
It is the full blown case where we consider every final possible force which can act on the system. The differential equation in this case, Mu'' + γu' + ku = F( t) The displ
x=±4, if -2 = y =0 x=±2, if -2 = y = 0
1. How many closed necklaces of length 7 can be made with 3 colors? (notice that 7 is a prime) 2. How many closed necklaces of length 10 can be made with 3 colors (this is di erent
limit x APProaches infinity (1+1/x)x=e
The Limit : In the earlier section we looked at some problems & in both problems we had a function (slope in the tangent problem case & average rate of change in the rate of chan
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