Question

How do you evaluate the definite integral `int 4x-5` from `[1,2]`?

Answer 1

`1`.

Explanation:

Recall the Fundamental Principle of Definite Integration :

`if intf(x)dx=F(x)+C, then, int_a^bf(x)dx=F(b)-F(a)=[F(x)]_a^b`.

`int(4x-5)dx=4x^2/2-5x+C=2x^2-5x+C`

`:. int_1^2(4x-5)dx=[2x^2-5x]_1^2=[(8-10)-(2-5)]=-2+3=1`.