Grade 12Integral Calculus

lim {(integration of F(t) dt) 4m 2 to sec^2 x} divided by {x^2- pi^2/16}

x->pi/4

shubhra pathak

15 Years agoGrade 12

12 Years ago

Ans: 0

Sol:

$L = \lim_{x\rightarrow \frac{\pi }{4}}\frac{\int_{2}^{sec^{2}x}F(x)dx}{x^{2}-\frac{\pi ^{2}}{16}}$

It is zero by zero form. So apply L’hospital rule.

$L = \lim_{x\rightarrow \frac{\pi }{4}}\frac{F(sec^{2}x)-F(2)}{2x} = \frac{F(2)-F(2)}{2.\frac{\pi }{4}}$

$L = 0$

Thanks & Regards

Jitender Singh

IIT Delhi

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