If f ( x ) is a polynomial and if lim t → a ( t − a ) 3 ∫ a t f ( x ) dx − ( 2 t − a ) ( f ( t ) + f ( a )) = 0 for all a , then the degree of f ( x ) can atmost be - [0pt]

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Suppose we define the definite integral using the following formula:

$\int_{a}^{b} f (x) d x = \frac{b - a}{2} (f (a) + f (b))$

For a more accurate result, for $c \in (a, b)$ , we have:

$F (c) = \frac{c - a}{2} (f (a) + f (c)) + \frac{b - c}{2} (f (b) + f (c))$

When $c = \frac{a + b}{2}$ , we get:

$\int_{a}^{b} f (x) d x = \frac{b - a}{4} (f (a) + f (b) + 2 f (c))$

If $f (x)$ is a polynomial and if $lim_{t \to a} \frac{\int _{a}^{t} f ( x ) dx - ( \frac{t - a}{2} ) ( f ( t ) + f ( a ))}{( t - a ) ^{3}} = 0$ for all a , then the degree of $f (x)$ can atmost be - [0pt]

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

⏱ 2mℹ️ Source: QB

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