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Question Number 150585 by bekzodjumayev last updated on 13/Aug/21

lim_(x→0) ((∫_0 ^π cosx^2 dx)/x)=?? Help

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\underset{\mathrm{0}} {\overset{\pi} {\int}}{cosx}^{\mathrm{2}} {dx}}{{x}}=?? \\ $$$${Help} \\ $$

Commented by mr W last updated on 13/Aug/21

lim_(x→0) ((∫_0 ^π cosx^2 dx)/x) =lim_(x→0) ((constant)/x) =∞

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\underset{\mathrm{0}} {\overset{\pi} {\int}}{cosx}^{\mathrm{2}} {dx}}{{x}} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{constant}}{{x}} \\ $$$$=\infty \\ $$

Commented by bekzodjumayev last updated on 13/Aug/21

Commented by bekzodjumayev last updated on 13/Aug/21

There is no such answer

$${There}\:{is}\:{no}\:{such}\:{answer} \\ $$

Commented by mr W last updated on 13/Aug/21

if the question is lim_(x→0) ((∫_0 ^π cosx^2 dx)/x)=? then all answers given are wrong.

$${if}\:{the}\:{question}\:{is}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\underset{\mathrm{0}} {\overset{\pi} {\int}}{cosx}^{\mathrm{2}} {dx}}{{x}}=? \\ $$$${then}\:{all}\:{answers}\:{given}\:{are}\:{wrong}. \\ $$

Commented by ajfour last updated on 13/Aug/21

the constant might just be zero, i could not check; but i think it requires cos [(π−t)^2 ]=−cos t^2

$${the}\:{constant}\:{might}\:{just}\:{be}\: \\ $$$${zero},\:{i}\:{could}\:{not}\:{check};\:{but}\:{i} \\ $$$${think}\:{it}\:{requires} \\ $$$$\mathrm{cos}\:\left[\left(\pi−{t}\right)^{\mathrm{2}} \right]=−\mathrm{cos}\:{t}^{\mathrm{2}} \\ $$

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