Question

6 points s More than one option, Students must investigate all options. Wrong answer have negative marks. For finding the volume of the structure under the surface z = e-x?-V and above the disc x? +y+s4, following integrations can be use A. 21 2 dzdrde B e-(x2+77)dydx -4-x? rdz drde D 210 ° "/ST " See LLL **. azayox -Parde E e-(x2+ v)dydx

Answer 1

For finding the volume of the structure under the Surface Z= e 2² y 2 and above the disc x² + y224 following integrations can be use Amy :-) Im Cartesian Coordinate system: V- SSJ du= dz dy dla Z V Z=e-иа 2 2 Ja-n2 SIS da dyda - 2 n²ty2=4 -J4-12 O = option [E] is correct Ja-n2 v= 2 e z] dydn O -2 - S4-12 2 9-12 e-(4²4y?) dydn - 2 q-12 - Ja =) option [B.] is correct.

We use Property of definite integral. q 9 fludra 2 2 jf f(x) dx if f(-4)= f(n) i. e. f is even function 2 4-12 v=2x2 e-(x?ty 2) dyda 0 [vo e e-(x²+4) is even function] V 4 2 4-12 - (+²+ y2) e dyda =) option [f.] is correct. Now Im Cylindrical coordinato & System n = rcoso, y = r Simo, 2=2 hence oers 2, osoL 27, § 2 2=0-1?y2 oczce-k? dua r dz drdo

So volume is 2T 2 eez v= SL a da drdo option [..] is correct. =) option [B.], [C], [E] and [F.] is correct.