Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Use (11.6) and (11.14) to (11.16) to evaluate the following integrals. Warning hint: See comments just after (11.6) and (11.16) about the range of integration. 15. (c) / e*s'(z) dz

Use (11.6) and (11.14) to (11.16) to evaluate the following integrals. Warning hint: See comments just after (11.6) and (11.16) about the range of integration. 15. (c) / e*s'(z) dz

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 19E
See similar textbooks
icon
Related questions
Question
100%

Please solve question 15

[ «95(2 – to) dt = { dlto), a<to <b, $(t)8(t – to) dt = { (11.6) 0, otherwise. Derivatives of the o Function To see that we can attach a meaning to the derivative of 8(x – a), we write $(x)8'(x – a) dx and integrate by parts to get (11.14) (x)8'(x-a) dr = 0(x)d(x-a) -| (x)(x- a) dr = -o'(a). The integrated term is zero at too, and we evaluated the integral using equation (11.6). Thus, just as 8(x – a) “picks out" the value of o(x) at x = a [see equation (11.6)], so d'(x - a) picks out the negative of o (x) at r = a. Integrating by parts twice (Problem 14), we find (11.15) I «(x)8"(x – a) dr = ¢" (a). Repeated integrations by parts gives the formula for the derivative of any order of the d function (Problem 14): (11.16) / $(x)6{») (x – a) dz = (-1)"ø(") (a). Use (11.6) and (11.14) to (11.16) to evaluate the following integrals. Warning hint: See comments just after (11.6) and (11.16) about the range of integration. 15. (e) L * xp (x),8 =g
Transcribed Image Text:[ «95(2 – to) dt = { dlto), a<to <b, $(t)8(t – to) dt = { (11.6) 0, otherwise. Derivatives of the o Function To see that we can attach a meaning to the derivative of 8(x – a), we write $(x)8'(x – a) dx and integrate by parts to get (11.14) (x)8'(x-a) dr = 0(x)d(x-a) -| (x)(x- a) dr = -o'(a). The integrated term is zero at too, and we evaluated the integral using equation (11.6). Thus, just as 8(x – a) “picks out" the value of o(x) at x = a [see equation (11.6)], so d'(x - a) picks out the negative of o (x) at r = a. Integrating by parts twice (Problem 14), we find (11.15) I «(x)8"(x – a) dr = ¢" (a). Repeated integrations by parts gives the formula for the derivative of any order of the d function (Problem 14): (11.16) / $(x)6{») (x – a) dz = (-1)"ø(") (a). Use (11.6) and (11.14) to (11.16) to evaluate the following integrals. Warning hint: See comments just after (11.6) and (11.16) about the range of integration. 15. (e) L * xp (x),8 =g
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer