Question

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

Answer 1

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 = \(\int_a^b\)f(x)dx-\(\int_a^b\)g(x)dx