Consider the function g (x) = 5x2-18x+35. find the area under the curve g (x) from x = 0 to x = 13 and then subtract from it the area under the same curve g (x) from x = 0 to x=1. what is the difference?

We integrate the given equation such that,

integral of g (x) = (5/3) x³ - 9x² + 35x

Substituting,

x = 13

integral of g (x) = (5/3) (13³) - 9 (13) ² + 35 (13)

= 2595.67

and, x = 0

integral of g (x) = 0

The area is 2595.67 - 0 = 2595.67

For the second part,

x = 1

integral of g (x) = (5/3) (1) ³ - 9 (1) ² + 35 (1)

= 27.67

Area under the curve between x = 0 and x = 1 is 27.67

The difference between the two areas is,

2595.67 - 27.67 = 2568.0

Answer: 2568.0 units squared