Properties of Integrals

Properties of Integrals

(1) If k is any constant, then  âˆ« kf ( x)dx   k ∫f ( x)dx

(2) ∫ ( f1 (x) ± f2 (x))dx = ∫ f1 (x)dx ±∫ f2 (x)dx

Note 11.1

The above two properties can be combined and extended as

∫ ( k1 f1 ( x ) ± k 2 f 2 ( x ) ± k 3 f 3 ( x ) ±. . .± k n f n ( x )) dx

= k1 ∫ f1 ( x ) dx ± k 2 ∫ f 2 ( x ) dx ± k 3 ∫ f 3 ( x )dx ±. . .± k n ∫ f n ( x ) dx.

That is, the integration of the linear combination of a finite number of functions is equal to the linear combination of their integrals

Example 11.8

Integrate the following with respect to x:

EXERCISE 11.3

Integrate the following with respect to x: