Integral of f'(x) given a table with x and f(x)

Question

I was given a table with

x= 0,3,5,7,8, and 12

f(x)=67,58,51,46,44, and 39 respectively

The problem asks me to find the integral from 0 to 12 of f'(x). I know that the integral and derivative cancel each other out but I'm still really confused.

Answer 1

hi,

As you know the meaning of integral:

∫​f′(x)dx=f(b)−f(a)

as you know bounded of integral is a= 0 and b = 12 so

∫​f′(x)dx=f(b)−f(a) = f(12)−f(0) = 39 - 67 = -28

I hope it is useful,

Minoo

Answer 2

See the videa.