Let ' f ' be a continuous function such that sgn (( f ( x ) − 1 ) ( f ( x ) − 2 )) < 0∀ x ∈ ( 4 , 8 ) , then [ 4 1 ∫ 4 8 f ( x ) dx ] is (where sgn is signum function \& [.] is greatest integer function) -

1 < f ( x ) < 2 ⇒ 4 < ∫ 4 8 f ( x ) dx < 8 ⇒ 1 < 4 1 ∫ 1 4 f ( x ) dx < 2 ⇒ [ 4 1 ∫ 1 4 f ( x ) dx ] = 2

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

Let ' $f$ ' be a continuous function such that $sgn ((f (x) - 1) (f (x) - 2)) < 0\forall x \in (4, 8)$ , then $[\frac{1}{4} \int_{4}^{8} f (x) dx]$ is (where sgn is signum function \& [.] is greatest integer function) -

Options:

Answer:

Solution:

$1 < f (x) < 2 \Rightarrow 4 < \int_{4}^{8} f (x) dx < 8 \Rightarrow 1 < \frac{1}{4} \int_{1}^{4} f (x) dx < 2 \Rightarrow [\frac{1}{4} \int_{1}^{4} f (x) dx] = 2$

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...