Question

What is the reverse integral property of definite integrals?

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

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

(c) \(\int_a^b\)f(x)dx=\(\int_b^a\)g(x)dx

(d) \(\int_a^b\)f(x)dx=-\(\int_b^a\)f(x)dx

I have been asked this question during an online exam.

I need to ask this question from Properties of Definite Integrals in section Integrals of Mathematics – Class 12

Answer 1

Correct option is (d) \(\int_a^b\)f(x)dx=-\(\int_b^a\)f(x)dx

Best explanation: In the reverse integral property the upper limits and lower limits are interchanged. The reverse integral property of definite integrals is \(\int_a^b\)f(x)dx=-\(\int_b^a\)f(x)dx.