The region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.
In this question,
The curves are y = 2/x, y = 2/x^2, x = 4
The diagram below shows the region enclosed by the given curves.
From the diagram, the limit of x is from 1 to 4.
The given curves are integrated with respect to x and the area is calculated as
![A=\int\limits^4_1 {\frac{2}{x} } \, dx -\int\limits^4_1 {\frac{2}{x^{2} } } \, dx](https://tex.z-dn.net/?f=A%3D%5Cint%5Climits%5E4_1%20%7B%5Cfrac%7B2%7D%7Bx%7D%20%7D%20%5C%2C%20dx%20-%5Cint%5Climits%5E4_1%20%7B%5Cfrac%7B2%7D%7Bx%5E%7B2%7D%20%7D%20%7D%20%5C%2C%20dx)
⇒ ![A=2[\int\limits^4_1 {\frac{1}{x} } \, dx -\int\limits^4_1 {\frac{1}{x^{2} } } \, dx]](https://tex.z-dn.net/?f=A%3D2%5B%5Cint%5Climits%5E4_1%20%7B%5Cfrac%7B1%7D%7Bx%7D%20%7D%20%5C%2C%20dx%20-%5Cint%5Climits%5E4_1%20%7B%5Cfrac%7B1%7D%7Bx%5E%7B2%7D%20%7D%20%7D%20%5C%2C%20dx%5D)
⇒ ![A=2[\int\limits^4_1( {\frac{1}{x} } - {\frac{1}{x^{2} } } )\, dx]](https://tex.z-dn.net/?f=A%3D2%5B%5Cint%5Climits%5E4_1%28%20%7B%5Cfrac%7B1%7D%7Bx%7D%20%7D%20%20-%20%7B%5Cfrac%7B1%7D%7Bx%5E%7B2%7D%20%7D%20%7D%20%29%5C%2C%20dx%5D)
⇒ ![A=2[lnx-\frac{1}{x} ] \limits^4_1](https://tex.z-dn.net/?f=A%3D2%5Blnx-%5Cfrac%7B1%7D%7Bx%7D%20%5D%20%5Climits%5E4_1)
⇒ ![A=2[(ln4-\frac{1}{4} )-(ln1-\frac{1}{1} )]](https://tex.z-dn.net/?f=A%3D2%5B%28ln4-%5Cfrac%7B1%7D%7B4%7D%20%29-%28ln1-%5Cfrac%7B1%7D%7B1%7D%20%29%5D)
⇒ A = 2[(1.3862-0.25) - (0-1)]
⇒ A = 2[1.1362 + 1]
⇒ A = 2[2.1362]
⇒ A = 4.2724 square units.
Hence we can conclude that the region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.
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7:50 plus 2 hrs = 9:50
9:50 plus 28 min= 10:18 pm
Hello,
Answer D 5/4
since div 15={1,3,5,15}
and div 8={1,2,4,8}
posiible rational root is a*b where a∈div 15 and b∈div 8
The difference between crystalline and amorphous polymers is that in crystalline polymers, the atoms are arranged in a regular pattern such that every part of the pattern is homogenous, while amorphous has irregular lattices.
Do both as equation it will make it easier for her