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3.4b Laws of Definite Integrals

3.4b Laws of Definite Integrals




Example:
Given that 37f(x)dx=5 , find the values for each of the following:

(a)376f(x)dx(b)37[3f(x)]dx(c)732f(x)dx(d)34f(x)dx+45f(x)dx+37f(x)dx(e)37f(x)+72dx


Solution:
(a)376f(x)dx=637f(x)dx=6(5)=30(b)37[3f(x)]dx=373dx37f(x)dx=[3x]375=[3(7)3(3)]5=7(c)732f(x)dx=372f(x)dx=237f(x)dx=2(5)=10(d)34f(x)dx+45f(x)dx+37f(x)dx=37f(x)dx=5(e)37f(x)+72dx=37[12f(x)+72]dx=3712f(x)dx+3772dx=1237f(x)dx+[7x2]37=12(5)+[7(7)27(3)2]=52+14=1612


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