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Method of cylinders or method of shells
The formula for the area in all of the cases will be,
A = 2 ∏ ( radius ) (height )
There are some important differences among this method & the method of rings/disks that we have to note before moving on. Firstly, rotation around a vertical axis will give an area which is a function of x and rotation around a horizontal axis will give an area which is a function of y. It is exactly opposite of the method of rings/disks.
Secondly, we don't take the total range of x or y for the limits of integration. Rather than we take a range of x or y which will cover one side of the solid. If we expand out the radius to cover one side automatically we will expand in the other direction as well to cover the other side.
Example 1 Add 4x 4 + 3x 3 - x 2 + x + 6 and -7x 4 - 3x 3 + 8x 2 + 8x - 4 We write them one below the other as shown below.
In this section we will consider for solving first order differential equations. The most common first order differential equation can be written as: dy/dt = f(y,t) As we wil
Determine the mean of the subsequent numbers: Example: Determine the mean of the subsequent numbers: 5, 7, 1, 3, 4 Solution: where x' =
please i need the answers to x^_7x+10 i want the vertex,axis of semetery,y intersect and the x intercept
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limit x APProaches infinity (1+1/x)x=e
Arc Length - Applications of integrals In this part we are going to look at determining the arc length of a function. As it's sufficiently easy to derive the formulas that we'
who discovered unitary method??
#k1=f(Tn, Xn), k2=f (Tn + H.Y,Xn + H.Y.k1) Xn+1=Xn + H(a.k1+ b.k2) Find a relation between Y,a and b so that the method is second order consistent.
A 3 km pipe starts from point A end at point B Population = 3000 people Q = 300 L/day/person Roughness = cast ion pipe Length of the pipe = 3km Case 1 From A to B
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