Question

Find the area of the region lying to the right of x = y² − 1 and to the left of x = 7 − y².

Answer 1

To find the area of the region between the two curves, set the equations equal to each other to find the points of intersection. Then integrate the difference of the two equations with respect to y and calculate the area.

Step-by-step explanation:

To find the area of the region between the two curves, we need to find the points of intersection first. Setting the two equations equal to each other, we have y² - 1 = 7 - y². Simplifying, we get y = ±√3. Now we can find the area by integrating the difference of the two equations with respect to y from -√3 to √3. The integral is:

∫(7 - y²) - (y² - 1) dy from -√3 to √3

After integrating and calculating, the area between the two curves is 14√3 square units.