Question

Find the total area of the regions enclosed by the curve y=x^4-x^3, the x axis and the line x=2.

the answer should be 2.5

Answer 1

integrate from y from 0 to 2, but you might want to check for any x intercepts along the interval

Answer 2

y factors as

y = x^3 (x-1)

y = 0 when x=0 and x=1, so you will simply have two integrations to deal with

Answer 3

1/20 + 49/20 = 50/20, 5/2

since it asks for the area, area is always positive. otherwise we would simply integrate from 0 to 2 and get about 2.4 which is a measure of displacement.