What is the difference property of definite integrals?

Category: QuestionsWhat is the difference property of definite integrals?
Editor">Editor Staff asked 11 months ago

What is the difference property of definite integrals?
 
(a) \int_a^b[-f(x)-g(x)dx
 
(b) \int_a^b[f(-x)+g(x)dx
 
(c) \int_a^b[f(x)-g(x)dx
 
(d) \int_a^b[f(x)+g(x)dx
 
I have been asked this question in semester exam.
 
This intriguing question comes from Properties of Definite Integrals topic in portion Integrals of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

The correct option is (c) \int_a^b[f(x)-g(x)dx
 
The explanation is: The sum difference property of definite integrals is \int_a^b[f(x)-g(x)dx
 
\int_a^b[f(x)-g(x)dx = \int_a^bf(x)dx-\int_a^bg(x)dx