Question

Evaluate \(\int_3^7\)2f(x)-g(x)dx, if \(\int_3^7\)f(x) = 4 and \(\int_3^7\)g(x)dx = 2.

(a) 38

(b) 12

(c) 6

(d) 7

This question was addressed to me in a job interview.

Enquiry is from Properties of Definite Integrals topic in chapter Integrals of Mathematics – Class 12

Answer 1

The correct choice is (c) 6

To elaborate: \(\int_3^7\)2f(x)-g(x)dx = 2 \(\int_3^7\)f(x)  – \(\int_3^7\)g(x)dx

= 2(4) – 2

= 6