Find the area between y=x^2 and y=x^3 on [0,1]

Question

Distance between curves is by far the hardest section in my book! If possible show me a video again! This is the best website for help that teaches you the method instead of belittling you and bashing you for not understanding. Thank you Wyzant team!

Answer 1

The area between 2 functions is the integral of the difference between the functions, evaluated over a specified interval.

Graph the functions to determine if the integration must be done in 2 steps. (In this case, it does not)

Area = (integral from 0 to 1) of x^3 - x^2

The integral is 1/4 * x^4 - 1/3 * x^3 (Since we will integrate between 2 points, we do not need the constant of integration)

The value for x = 0 is 0, so our answer is simply |1/4 - 1/3| = 1/12