CPM Homework Help : CALC3RD Problem 6-98

Calculate the area (shown in the diagram) between the graphs of $y=\frac{1}{x^2+1}$ and $y = x^2$ .

Step 1:

Identify which function is on top and which is on the bottom.

Step 2:

$\text{Area between curves}=\int_{A}^{B}((\text{top function})-(\text{bottom function}))dx$

$A =$ left intersection point
$B =$ right intersection point

Upward parabola, vertex at the origin, & a curve, coming from left above x axis, concave up, turning at the point (0, comma 1), continuing to the right above x axis, changing concavity at approximate points, (negative 1, comma 0.5) & at (1, comma 0.5), curves intersect at approximate points (negative 0.9, comma 0.6), & (0.9, comma 0.6), with shaded region between curves & intersection points.