{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ImproperIntegral

ImproperIntegral - Improper Integral Since the concept of...

This preview shows pages 1–2. Sign up to view the full content.

Improper Integral Since the concept of Laplace transform involves an integral from zero to infinity, the knowledge of improper integral is needed. Definition : An improper integral over an unbounded interval is defined as a limit of integrals over finite intervals; thus f(t)dt a ! " = lim A #! f(t)dt a A " where A is a positive real number. If the integral from a to A exists for each A > a, and if the limit as A exists, then the improper integral is said to converge to that limiting value. Otherwise the integral is said to diverge , or fail to exist, Examples : 1) Let f(t) = e ct , t 0 and c is a real nonzero constant. e ct dt = lim A !" e ct dt = lim A !" 0 A # 0 " # e ct c 0 A = lim A !" 1 c e cA \$ 1 ( ) if c < 0 , e cA 0 as A , then the improper integral converges to -1/c, if c > 0, e cA as A , then the improper integral diverges, if c = 0 , e ct = 1, then the improper integral diverges. 2) Let f(t) = 1/t, t

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 3

ImproperIntegral - Improper Integral Since the concept of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online