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Question Number 168772 by Dildora last updated on 17/Apr/22

Commented by safojontoshtemirov last updated on 18/Apr/22

$S = 4 \underset{0}{\int^{\frac{π}{2}}} \sqrt{{({(e^{t} s i n t)}^{'})}^{2} + {({(e^{t} c o s t)}^{'})}^{2}} d t$ $S = 4 \underset{0}{\int^{\frac{π}{2}}} \sqrt{{(e^{t} s i n t + e^{t} c o s t)}^{2} + {(e^{t} c o s t - e^{t} s i n t)}^{2}} d t$ $S = 4 \underset{0}{\int^{\frac{π}{2}}} \sqrt{e^{2 t} ({s i n}^{2} t + 2 s i n t \cdot c o s t + {c o s}^{2} t + {c o s}^{2} t - 2 s i n t \cdot c o s t + {c o s}^{2} t)} d t$ $S = 4 \sqrt{2} \underset{0}{\int^{\frac{π}{2}}} e^{t} d t = 4 \sqrt{2} e^{t} \underset{0}{\overset{\frac{π}{2}}{∣}} = 4 \sqrt{2} (\sqrt{e^{π}} - 1)$
	Answered by alephzero last updated on 17/Apr/22

	$? ? ?$
	Commented by Dildora last updated on 17/Apr/22

	$t h e v o l u m e o f a n o b j e c t f o r m e d b y r o t a t i n g i t a r o u n d a n a x i s$
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