Question

Change the Cartesian integral to an equivalent polar integral, and then evaluate. ss dx dy -V16-y2 1+122 7:18 +2 1n 5) 2 (8 +2 In 5) 4 (8 + In 5) 78 +in5) 2

Answer 1

given: Jiezty didy 1 Now form In It Jarryd - J16-ya will change it in polar polar 8. x2ty? rloso y = r Sino dody = verde J16-y2 Sem - circle (left handed) Here 2- is ។ Region of integration Here is -4 going from 2/2 to 37 is gong flom to y and 7 O

२०० in balar form integral become ४ Iar rardo 3TV 9 82 drde - tr T/2 Substitute u=rt! Put dr and g 2 = (4-17² Wher rao u=1 8=4 4.5 (4-1² dy do 3113 f T12 Now expand asa dy do 31112 s S (U+1 - 2) dy is 11.

31/2 SE udut dy atide ja idy lode П. 31/2 s 1) SHT + Penugs - T24]s de TIL 3TT/ as the t In(o)-0(1) -(10 g).de دا ) 3152 g. In(s) ty.de 1/2 31/2 [[ln (0)44) IT T12 = In(s)ty (II) - Bo (ens + y)

= I (ln(s) ty) IT (In(s)+4) . spoo 1 ( 8+ lnls) q Answer