Question

Find the area between the curves y = x and y = x².

Answer 1

y = x is line with pts (0, 0) (-1, 1) (1, 1) (2, 2) etc

y = x² is parabola with vertex (0,0) up ward parabola 

They meet at pts (0, 0) and (1, 1)

⇒ y = x putting in y = x² 

x = x² ⇒ x = 0 ⇒ y = 0 

x =1 ⇒ y = 1 

Area is (shaded one) = (Area under line x = 0 to x = 1) – (Area under parabola x = 0 to x = 1)