solut2 - Homework 2- Solutions. 1. f ( x ) = 1 x ( x 2- x-...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework 2- Solutions. 1. f ( x ) = 1 x ( x 2- x- 6) = 1 x ( x + 2)( x- 3) = A x + B x + 2 + C x- 3 . Equations for the coefficients: x 2 ( A + B + C ) = 0 , x (- A- 3 B + 2 C ) = 0 , 1 (- 6 A ) = 1 . Solve: A =- 1 / 6, B = 1 / 10, C = 1 / 15. Have the indefinite integral, Z - 1 6 x + 1 10 1 x + 2 + 1 15 1 x- 3 dx =- 1 6 log | x | + 1 10 log | x + 2 | + 1 15 log | x- 3 | . Next, we evaluate the definite integral.- 1 6 log | x | fl fl fl fl 2 1 =- 1 6 (log2- log1) =- 1 6 log2 . 1 10 log | x + 2 | fl fl fl fl 2 1 = 1 10 (log4- log3) = 1 10 log(4 / 3) . 1 15 log | x- 3 | fl fl fl fl 2 1 = 1 15 (log1- log2) =- 1 15 log2 . All together,- 1 6 log2 + 1 10 log(4 / 3)- 1 15 log2 =- 7 30 log2 + 1 10 log(4 / 3) . 4 Section 3.2, Problem 32. Write down the right hand side in terms of the Heaviside function, f ( t ) = 12 H ( t- 4) . Calculate Laplace of f ( t ): L [ f ] = L [12 H ( t- 4)] = 12 L [ H ( t- 4)] = 12 1 s e- 4 s , 1 see Example 3.11. Take Laplace of both sides of the equation. Set L...
View Full Document

Page1 / 3

solut2 - Homework 2- Solutions. 1. f ( x ) = 1 x ( x 2- x-...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online