Answer is: option3
4a - 7bSolution:
Given Integral:
\[ \int_a^b f(x)\,dx = 2a - 5b \]
Compute the Integral of the Constant:
\[ \int_a^b 2\,dx = 2(b - a) \]
Set Up the Desired Integral:
\[ \int_a^b [f(x) - 2]\,dx = \int_a^b f(x)\,dx - \int_a^b 2\,dx \]
Substitute the Known Values:
\[ \int_a^b [f(x) - 2]\,dx = (2a - 5b) - 2(b - a) \]
Simplify the Expression:
\[ \int_a^b [f(x) - 2]\,dx = 2a - 5b - 2b + 2a = 4a - 7b \]
Final Answer:
\[ \boxed{4a - 7b} \]
Correct Option: (C) \( 4a - 7b \)