Step-by-step explanation:
[tex] \frac{dA}{dx} = 3 {(x - 1)}^{2} \\A = ∫3 {(x - 1)}^{2}dx \\ = ∫3 {x}^{2} - 6x + 3 \: dx \\ = \frac{3 {x}^{3} }{3} - \frac{6 {x}^{2} }{2} + 3x + c \\ = {x}^{3} - 3 {x}^{2} + 3 + c[/tex]
Now substitute in A=10 and X=3, to find the value of c
[tex]10 = {3}^{3} - 3 {(3)}^{2} + 3(3) + c \\ c = 1[/tex]
Hence,
[tex]A = {x}^{3} - 3 {x}^{2} + 3x + 1[/tex]
