Question

need help finding the area between y=x, and y=x^2-2
ans:4.5

Answer 1

The y =x is the greater function, so you'll subtract the area under x^2-2 from the area under x. See the graph: https://www.google.com/search?q=x%2C+x%5E2-2&aq=f&oq=x%2C+x%5E2-2&aqs=chrome.0.57j65j0l3j62.625&sourceid=chrome&ie=UTF-8

Find the two points of intersection a and b (by letting x = x^2 - 2) and those will be your limits of integration. Then you find the area by subtracting the x^2 - 2 from x:

\[\int\limits_{a}^{b} \left( x - (x^2 - 2) \right)dx\]