If f ( x ) = ∫ 0 x t s i n t d t , which of the following is true :-

f ′ ( x ) = x s i n x > 0 ⇒ f ( x ) is increasing in ( 0 , π ) f ′ ( x ) = x s i n x < 0 ⇒ f ( x ) is decreasing in ( π , 2 π )

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

If $f (x) = \int_{0}^{x} \frac{s i n t}{t} d t$ , which of the following is true :-

Answer:

Solution:

$f^{'} (x) = \frac{s i n x}{x} > 0 \Rightarrow f (x)$ is increasing in $(0, π)$

$f^{'} (x) = \frac{s i n x}{x} < 0 \Rightarrow f (x)$ is decreasing in $(π, 2 π)$

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

⏱ 2mℹ️ Source: QB

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