Question

What is the area under the graph of f(x) = (3/x²) - 1 evaluated from x = 1 to x = 2.

Answer 1

To find the area under the graph we need to calculate the integral:

`\int_1^2((3)/(x^2)-1)dx`

So let's calculate the integral:

`\begin{gathered} \int_1^2((3)/(x^(2))-1)dx=(-(3)/(x)-x)\vert_1^2 \\ =(-(3)/(2)-2)-(-3-1) \\ =-(7)/(2)+4 \\ =(1)/(2) \end{gathered}`

Therefore, the area under the graph is 1/2