Sketch and Find the area of the region determined by the intersections of the curves.
y= (2/(x^{2}+1)), y=(absolute value of) x
I do not know how to proceed. The book I am using is of no help. Perhaps a push in the right direction is in order?
Sketch and Find the area of the region determined by the intersections of the curves.
y= (2/(x^{2}+1)), y=(absolute value of) x
I do not know how to proceed. The book I am using is of no help. Perhaps a push in the right direction is in order?
That's not entirely correct. You need to split it into two separate integrals because the function on the right side is x and the function on the left side is -x.
Technically the below is correct:
$\displaystyle \int_{-1}^{1} \frac{2}{1+x^2} - \left | x \right | dx$
But that's not what you did - you dropped the absolute value.
You have already been told that in order to evaluate this area, you need to do TWO integrals, because the absolute value function is actually a HYBRID function, $\displaystyle \displaystyle \begin{align*} |x| = \begin{cases} \phantom{-} x \textrm{ if } x \geq 0 \\ -x \textrm{ if } x < 0 \end{cases} \end{align*}$, so you will need to perform an integral for EACH of those cases.