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Chapter: 11th Mathematics : UNIT 11 : Integral Calculus

Properties of Integrals

two properties can be combined and extended as below

Properties of Integrals


(1) If k is any constant, then  ∫ 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:



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11th Mathematics : UNIT 11 : Integral Calculus : Properties of Integrals |


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