Question

How do you find the area under the graph of `f(x)=e^(-2lnx)` on the interval [1, 2]?

Answer 1

`1/2`

Explanation:

`f(x) = e^{-2ln x} = x^-2`

Thus the area under the curve is

`int_1^2 f(x) dx = int_1^2 x^-2 dx`
`qquad = (-x^-1)_1^2`
`qquad = -1/2-(-1/1) = 1-1/2=1/2`