Find the area between the graph of the function and the x-axis over the given interval, if possible.
f(x) = 5/(x-2)^2 for (-[infinity], 1)

So then the integral converges and the area below the curve and the x axis would be 5.

Step-by-step explanation:

In order to calculate the area between the function and the x axis we need to solve the following integral:

For this case we can use the following substitution and we have

And if we solve the integral we got:

And we can rewrite the expression again in terms of x and we got:

And we can solve this using the fundamental theorem of calculus like this:

So then the integral converges and the area below the curve and the x axis would be 5.

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .