Find the area between the graph of the given function and the x-axis over the given interval, if possible.
1 answer:
Answer:
Area = 1
Step-by-step explanation:
Given that f(x) is a funciton as
![f(x) = \frac{1}{(x-1)^2}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B%28x-1%29%5E2%7D)
We have to find the area of the curve of the function above x axis between -infty and 0
Hence area required would be
![\int\limits^0_{-\infty} {\frac{1}{(x-1)^2} } \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E0_%7B-%5Cinfty%7D%20%20%7B%5Cfrac%7B1%7D%7B%28x-1%29%5E2%7D%20%7D%20%5C%2C%20dx)
Using power rule we get
integrate value is = (x-1)^(-1)
Substitute limits
For -infty this value is 0, but for x =0 this is -1
Hence area = 0-(-1) = 1
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