If F ( x ) = x 2 1 ∫ 4 x ( 4 t 2 − 2 F ′ ( t ) ) d t then F ′ ( 4 ) equals to -

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

If $F (x) = \frac{1}{x ^{2}} \int_{4}^{x} (4 t^{2} - 2 F^{'} (t)) d t$ then $F^{'} (4)$ equals to -

Answer:

Solution:

$F (4) = 0$

$x^{2} F (x) = \int_{4}^{x} (4 t^{2} - 2 F^{'} (t)) d t$

d.w.r. to $x$

$x^{2} F^{'} (x) + F (x) 2 x = 4 x^{2} - 2 F^{'} (x)$

put $x = 4$

$16 F^{'} (4) = 64 - 2 F^{'} (4$

$F^{'} (4) = \frac{32}{9}$ z`

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

⏱ 2mℹ️ Source: QB

Loading discussions...