Find area under the curve

Question

Find the area under the curve h(x)=(3x-2)^3 from x=1 to x=2

Answer 1

Use u substitution to integrate with 

 

u = 3x - 2

du/dx = 3

 

Area under the curve 

 

= integral (3x-2) from 1 to 2

 

= 1/3 ( u) du

 

= (u^2/6)

 

= (3x-2)^2 / 6

 

= [16/6] - [1/6]

 

= 15/6

 

= 5/2

 

= 2.5 units ^2