7.8.55-eg-1 - cosh 2 = e 2 + e-2 2 = e 4 + 1 2 e 2 cosh 1 =...

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

View Full Document Right Arrow Icon
Example Evaluate Z 1 1 / 2 sinh (1 /x ) x 2 dx . Make the substitution u = 1 x and du = - 1 x 2 , and adjust the limits of integration x = 1 / 2 u = 2 x = 1 u = 1 to obtain Z 1 1 / 2 sinh (1 /x ) x 2 dx = Z 2 1 sinh udu = cosh u ± ± ± ± ± 2 1 = cosh 2 - cosh 1 . Now evaluate hyperbolic cosine using exponentials:
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: cosh 2 = e 2 + e-2 2 = e 4 + 1 2 e 2 cosh 1 = e 1 + e-1 2 = e 2 + 1 2 e . Therefore, Z 1 1 / 2 sinh (1 /x ) x 2 dx = e 4-e 3-e + 1 2 e 2 ....
View Full Document

Ask a homework question - tutors are online