Question

Find the area of the shaded region
y= 2x/(x^2+4)
from x= -2 and x= 2
Note: People have been telling me that the two lines do not intersect but they do there has to be an answer. please help me.
Thanks

Answer 1

ln(x^2 + 4) = 0

Answer 2

well of course the lines x=2 and x=-2 do not intersect; they are parallel vertical lines. Not sure what that has to do with anything; the just set bounds to the region.

Since y is an odd function, and the bounds are symmetric about the y-axis, the integral will be zero.

Let u = x^2+4 and you just have

∫ du/u
Note that the limits of integration are now 8 and 8, so the integral is zero -- the area is symmetric above and below the x-axis.