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

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Answer 1 · 2016-09-11T16:23:29

$1$ $1$ .

Recall the Fundamental Principle of Definite Integration :

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

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

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

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