Question

Find the surface area generated by rotating the given curve about the y-axis. x = et - t, y = 4et/2, Osts5 €101-61 -541 X

Answer 1

solution: obtained surface Area (A) ay rotating une x= fit y = get tub t=a from about axis is given ofi A 2 2TY Jeg er av de dt کل in Gue casei o Q = S - S t notti = ex x2 he y=g

S A 2r༤-༤) -༤) 4 ༤_) + (4)) dt S > A འག) – ༤) -1） + dt (༥༩༦༤)4)) 2- A =(m)(༤ +) | ༤- ) + 72. dt S S ༤ A = (2) } (༤- ] ༤ ༽ - 2-༤ + ༥༩༦) dt S + A 2 ༤ (zr) } ༤ – ༤) + -ze F + het at S ན་ （ཀ) ） –༤) 24 titzet at

($ – s + s tetat ） S S C tat S ༩ tetat etat al at att (11) - Y S S A dt +P (+- བོ༽ - (1༤） - ) et tett) at tet (དuང) c A S -- ༤ - ༤) (༤ དྷ་) ༣༤ (515) A. AP （ | ( (༢-) ( ) A= beorts out butaide

Az 2T é -( :- - - - -65-9) A = 2h ( el + e -1 fet dt lets sole; tet at ; using integration by parts, S S tetat thetat Contests) Jetat) dt de S tet et) at 5 S oe) Jetat

s S Se ང et S - S - (s བ se S - S +། ནs + | - ܨ ܟܠ et at ༥S +། putting into equation ② 2 -༥༩ +1) – 《 A = 6T༥) - ) - ( ད དྷ ང - མ ཙང་མ་ ༠༣) s A

و .. ا) - ۸ A =(( ۱۰. | A (ملا۔ گے۔ -۱۹ )) A = π ۲( ۱° (2 - گے۔