Question

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?

Answer 1

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