Final answer:
To find the area of the region enclosed by the parabolas, solve for the intersection points and use integration.
Step-by-step explanation:
To find the area of the region enclosed by the parabolas, you need to determine the points of intersection between the two parabolas. Let's say the two parabolas are y = ax² + bx + c and y = dx² + ex + f. You can set these two equations equal to each other and solve for x to find the x-coordinates of the intersection points.
Once you have the x-values, you can substitute them back into either equation to find the corresponding y-values. Then, you can calculate the area of the enclosed region by taking the integral of the difference between the two parabolas over the interval defined by the x-values of the intersection points.
The complete question is: Find c > 0 such that the area of the region enclosed by the parabolas y = x^2 − c^2 and y = c^2 − x^2 is 140. C=?