Question

Help with q7 please !!

Answer 1

Explanation:

`(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`

Now substitute in A=10 and X=3, to find the value of c

`10 = {3}^(3) - 3 {(3)}^(2) + 3(3) + c \\ c = 1`

Hence,

`A = {x}^(3) - 3 {x}^(2) + 3x + 1`