Final answer:
To find the area between the curves y = -x and x = y^2 - 6, you need to determine the points of intersection and integrate the difference between the curves within those boundaries.
Step-by-step explanation:
The area between the curves y = -x and x = y^2 - 6 can be found by determining the points of intersection between the two curves and then integrating the difference between the curves within those boundaries. To find the points of intersection, set the two equations equal to each other:
-x = y^2 - 6
Now solve for y and substitute the value of y back into one of the original equations to find the corresponding x-value. Once you have the x-values of the points of intersection, integrate the difference between the curves from one point to the other to calculate the area between them.