Step 2
Let's set up the integral that will give us the area of the region that is bounded between y = 49 - x² and
y = x² - 1.
When we set up the integral, should we integrate with respect to x or with respect to y?
Since the height of the typical approximating rectangle is parallel to the y-axis, we should integrate
with respect to y.
Since the narrow width of the typical approximating rectangle is parallel to the x-axis, we should
integrate with respect to x.
Since the height of the typical approximating rectangle is parallel to the x-axis, we should integrate
with respect to x.
Since the narrow width of the typical approximating rectangle is parallel to the y-axis, we should
integrate with respect to y.
Hint: The narrow width of the typical approximating rectangle will represent the differential dx or the
differential dy. But which one? If the narrow width of the approximating rectangle is parallel to the x-axis,
it represents dx. But, if the narrow width of the approximating rectangle is parallel to the y-axis, it
represents dy.
The points of intersection will give us the indices of integration. What are the indices of integration? Enter
your answers as a comma separated list.
