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Volumes of Solids of Revolution / Method of Rings
In this section we will begin looking at the volume of solid of revolution. We have to first describe just what a solid of revolution is. To get a solid of revolution we begin with a function, y = f (x ) , on an interval [a,b].
Then we rotate this curve around a given axis to get the surface of the solid of revolution. For discussion let's rotate the curve around the x-axis, although it could be any vertical or horizontal axis. Carrying out this for the curve above gives the given three dimensional region.
writing sin 3 a.cos 3 a = sin 3 a.cos 2 a.cosa = sin 3 a.(1-sin 2 a).cosa put sin a as then cos a da = dt integral(t 3 (1-t 2 ).dt = integral of t 3 - t 5 dt = t 4 /4-t 6 /6
Properties 1. ∫ b a f ( x ) dx = -∫ b a f ( x ) dx . We can interchange the limits on any definite integral, all that we have to do is tack a minus sign onto the integral
if the sum of lengths of hypotenuse and a side of right triangle are given, prove the area of the triangle is maximum when angle between them is pi/3
A simple example of fraction would be a rational number of the form p/q, where q ≠ 0. In fractions also we come across different types of them. The two fractions
Related Rates : In this section we will discussed for application of implicit differentiation. For these related rates problems usually it's best to just see some problems an
Submit solutions for all of the following questions. Remember to set out your answers showing all steps completely and explicitly justify your steps. 1. Provide, in no more than
Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''s encountered is even or odd.on..
Applications of Integrals In this part we're going to come across at some of the applications of integration. It should be noted also that these kinds of applications are illu
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#sally wieghs 100kg. According to the 50/50 basal bolus rate be per meal bolus?
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