■ The ellipse is symmetric to both axes; hence the area inside the ellipse is four
times the area in the first quadrant.Evaluating Using a Graphing Calculator The calculator is
especially useful in evaluating definite integrals when the x-
intercepts are not easily determined otherwise or when an explicit
antiderivative of f is not obvious (or does not exist).
Example 1 __
Evaluate .
SOLUTION: The integrand has no easy antiderivative. The calculator
estimates the value of the integral to be 0.747 to three decimal places.
Example 2 __
In Figure N7–5, find the area under f (x) = −x^4 + x^2 + x + 10 and above the x-
axis.