If $f: D \in R$ be such that $f(x) = \sqrt {\sin (\cos x)} + \ln \left( { - 2{{\cos }^2}x + 3\cos x - 1} \right){\rm{, }}\,\,{\rm{then }}$ $\int_{{x_1}}^{{x_2}} {\left[ {\cos x - \frac{1}{2}} \right]} \,\,dx$ is equal to, where $x_1, x_2 \equiv D$ and [.] denotes the greatest integer function,

$\frac{1}{2}\left(x_2-x_1\right)$

$\frac{1}{2}\left(x_1-x_0\right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Medium

1 of 1

Analyzing +4 | -1

f: D \in R

be such that

f(x) = \sqrt {\sin (\cos x)} + \ln \left( { - 2{{\cos }^2}x + 3\cos x - 1} \right)\mathrm{, }\,\,\mathrm{then }

\int_{{x_1}}^{{x_2}} {\left[ {\cos x - \frac{1}{2}} \right]} \,\,dx

is equal to, where

x_1, x_2 \equiv D

and [.] denotes the greatest integer function,

View answer and explanation

Correct option: A

Option A (0) is correct because the greatest integer function evaluates to 0 within the domain, making the integral zero.