15_3_15 - dt 1 2 t 2 = √ 2 tan-1 √ 2 t ± ± ± ∞ =...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
15. The parabola z 2 = x 2 + y 2 , x + z = 1, can be parametrized in terms of y = t since ( 1 - x ) 2 = z 2 = x 2 + y 2 = x 2 + t 2 1 - 2 x = t 2 x = 1 - t 2 2 z = 1 - x = 1 + t 2 2 . Thus ds = t 2 + 1 + t 2 dt = 1 + 2 t 2 dt , and Z ds ( 2 y 2 + 1 ) 3 / 2 = Z -∞ 1 + 2 t 2 ( 2 t 2 + 1 ) 3 / 2 dt = 2 Z
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: dt 1 + 2 t 2 = √ 2 tan-1 ( √ 2 t ) ± ± ± ∞ = √ 2 π 2 = π √ 2 ....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online